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## Search Articles

2017, Graduate studies in mathematics, ISBN 9781470429522, Volume 178, xvi, 414 pages

Lorentz metrics, indefinite metrics | Classical differential geometry | Vector analysis | Differential geometry | Global analysis, analysis on manifolds | Local differential geometry | Surfaces in Euclidean space | Differential forms | Noncompact transformation groups | Exterior differential systems (Cartan theory) | Projective differential geometry | Frames (Vector analysis) | Homogeneous spaces | Geometry, Differential | Topological groups, Lie groups | Affine differential geometry | Local submanifolds | General theory of differentiable manifolds | Mathematical physics | Exterior differential systems | Differential invariants (local theory), geometric objects | Curves in Euclidean space

Book

2011, 6th ed., ISBN 0821852825, xv, 420

Book

1973, Cambridge monographs on mathematical physics., ISBN 0521200164, Volume 1, xi, 391

Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational...

Space and time | Astrophysics

Space and time | Astrophysics

Book

2002, Lecture notes in mathematics, ISBN 3540431446, Volume 1777., xii, 166

Book

Journal of geometry and physics, ISSN 0393-0440, 09/2010, Volume 60, Issue 9, pp. 1190 - 1208

In this paper we develop the theories of normed linear spaces and of linear spaces with indefinite metric, for finite dimensions both of which are also called Minkowski spaces in the literature...

Group of isometries | James orthogonality | Birkhoff orthogonality | Finsler space | Semi-definite inner product | Lorentz geometry | Minkowski space | Normed linear space | Indefinite inner product | Finite-dimensional real Banach space | Physical Sciences | Mathematics | Physics | Physics, Mathematical | Science & Technology | Mathematics - Metric Geometry

Group of isometries | James orthogonality | Birkhoff orthogonality | Finsler space | Semi-definite inner product | Lorentz geometry | Minkowski space | Normed linear space | Indefinite inner product | Finite-dimensional real Banach space | Physical Sciences | Mathematics | Physics | Physics, Mathematical | Science & Technology | Mathematics - Metric Geometry

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 03/2018, Volume 541, pp. 60 - 80

As is well known, for every orthogonal transformation of the Euclidean space there exists an orthogonal basis such that the matrix of the transformation is...

Cyclic spaces | Pseudo-Euclidean vector spaces | Jordan form | Linear transformations | Eigenvectors | Decomposition | Indefinite metrics | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Lorentz transformations | Euclidean geometry | Vector space | Linear algebra | Isomorphism | Eigenvalues | Subspaces | Invariants | Eigen values

Cyclic spaces | Pseudo-Euclidean vector spaces | Jordan form | Linear transformations | Eigenvectors | Decomposition | Indefinite metrics | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Lorentz transformations | Euclidean geometry | Vector space | Linear algebra | Isomorphism | Eigenvalues | Subspaces | Invariants | Eigen values

Journal Article

Journal of geometry and physics, ISSN 0393-0440, 08/2019, Volume 142, pp. 240 - 253

We study minimal Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric whose first normal space is two-dimensional and whose Gauss curvature K and normal curvature ϰ...

Minimal surfaces | Lorentz surfaces | Pseudo-Euclidean space with neutral metric | Physical Sciences | Mathematics | Physics | Physics, Mathematical | Science & Technology | Mathematics - Differential Geometry

Minimal surfaces | Lorentz surfaces | Pseudo-Euclidean space with neutral metric | Physical Sciences | Mathematics | Physics | Physics, Mathematical | Science & Technology | Mathematics - Differential Geometry

Journal Article

Publicationes mathematicae (Debrecen), ISSN 0033-3883, 2012, Volume 80, Issue 1-2, pp. 215 - 234

We extend to the semi-Riemannian context the well-known results obtained by Blair, Ludden and Yano on toroidal principal bundles endowed with a metric globally framed f-structure...

Principal bundle | Hopf fibration | Lorentz manifold | Indefinite metric | Globally framed f-structure | Physical Sciences | Mathematics | Science & Technology

Principal bundle | Hopf fibration | Lorentz manifold | Indefinite metric | Globally framed f-structure | Physical Sciences | Mathematics | Science & Technology

Journal Article

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică, ISSN 1224-1784, 06/2012, Volume 20, Issue 2, pp. 213 - 238

....
First is introduced the singular semi-Riemannian geometry for metrics which can change their signature...

Cauchy foliations | Schwarzschild black hole | Lorentz metrics | General relativity | singular semi-Riemannian geometry | degenerate metrics | Einstein equations | global hyperbolicity | indefinite metrics | Space-time singularities | black holes | Reissner-Nordström black hole | Kerr-Newman black hole | Black holes | Kerr-newman black hole | Reissner-nordström black hole | Global hyperbolicity | Degenerate metrics | Singular semi-riemannian geometry | Indefinite metrics | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Cauchy foliations | Schwarzschild black hole | Lorentz metrics | General relativity | singular semi-Riemannian geometry | degenerate metrics | Einstein equations | global hyperbolicity | indefinite metrics | Space-time singularities | black holes | Reissner-Nordström black hole | Kerr-Newman black hole | Black holes | Kerr-newman black hole | Reissner-nordström black hole | Global hyperbolicity | Degenerate metrics | Singular semi-riemannian geometry | Indefinite metrics | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

This bachelor thesis shows a way to classify second order symmetric tensors in the Lorentz metric...

Indefinite linear algebra | MATHEMATICS | symmetric tensors | classification of canonical form | Segre type | Minkowski space | Lorentz metric | MATEMATIK

Indefinite linear algebra | MATHEMATICS | symmetric tensors | classification of canonical form | Segre type | Minkowski space | Lorentz metric | MATEMATIK

Dissertation

Journal of the Chinese Chemical Society (Taipei), ISSN 0009-4536, 01/2016, Volume 63, Issue 1, pp. 11 - 19

In this communication we take up the significance and purpose of selecting the proper coordinate system from the flat space‐time of non‐relativistic theories...

Conjugate operators | Non‐positive metrics | Quantum theory | General relativity | Non-positive metrics | Physical Sciences | Chemistry | Chemistry, Multidisciplinary | Science & Technology | Algebra | Gravity | Lorentz transformations | Conjugates | Matrix algebra | Black holes | Relativity | Coordinates | Gravitational fields | Momentum | Equivalence principle | Operators (mathematics) | Mathematical analysis | Relativistic theory

Conjugate operators | Non‐positive metrics | Quantum theory | General relativity | Non-positive metrics | Physical Sciences | Chemistry | Chemistry, Multidisciplinary | Science & Technology | Algebra | Gravity | Lorentz transformations | Conjugates | Matrix algebra | Black holes | Relativity | Coordinates | Gravitational fields | Momentum | Equivalence principle | Operators (mathematics) | Mathematical analysis | Relativistic theory

Journal Article

Journal of geometry and physics, ISSN 0393-0440, 02/2017, Volume 112, pp. 85 - 94

....
These notions are designed to also make sense in cases when the Finslerian metric tensors are either not defined or degenerate along some directions in each tangent space...

Time orientability | Volume form | Lorentz–Finsler manifold | Physical Sciences | Mathematics | Physics | Physics, Mathematical | Science & Technology

Time orientability | Volume form | Lorentz–Finsler manifold | Physical Sciences | Mathematics | Physics | Physics, Mathematical | Science & Technology

Journal Article

Physical review. D, Particles and fields, ISSN 0556-2821, 02/1971, Volume 3, Issue 4, pp. 1046 - 1047

Journal Article

Geometriae dedicata, ISSN 0046-5755, 2/2002, Volume 89, Issue 1, pp. 57 - 105

.... To be specific, suppose that the Minkowski plane E
2
1 is the x,y-plane with metric dxdy. Our main theorem states that if ∂ℒ...

Geometry | indefinite metric | conformal geometric | Mathematics | Lorentz surface

Geometry | indefinite metric | conformal geometric | Mathematics | Lorentz surface

Journal Article

Physical review. D, Particles and fields, ISSN 0556-2821, 1973, Volume 8, Issue 6, pp. 1796 - 1807

Journal Article

Lettere al Nuovo cimento della Società italiana di fisica, ISSN 0375-930X, 08/1972, Volume 4, Issue 17, pp. 913 - 918

Journal Article

Physical review. D, Particles and fields, ISSN 0556-2821, 1977, Volume 15, Issue 2, pp. 416 - 425

Journal Article

Geometriae dedicata, ISSN 0046-5755, 2002, Volume 89, Issue 1, pp. 59 - 107

.... To be specific, suppose that the Minkowski plane E-1(2) is the x,y-plane with metric dxdy. Our main theorem states that if partial derivativeL is smoothable then L is conformally homeomorphic to the interior U of a Jordan curve in E-1(2...

Indefinite metric | Conformal geometric | Lorentz surface | Physical Sciences | Mathematics | Science & Technology

Indefinite metric | Conformal geometric | Lorentz surface | Physical Sciences | Mathematics | Science & Technology

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 1983, Volume 89, Issue 3, pp. 467 - 472

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2003, Volume 355, Issue 2, pp. 775 - 786

... in a (compact or noncompact) flat Lorentz 2-step nilmanifold N/\Gamma , where N is a simply connected 2-step nilpotent Lie group with a flat left-invariant Lorentz metric...

Geometry | Mathematical theorems | Algebra | Nonexistence | Spacetime | Inner products | Lie groups | Mathematical vectors | Curvature | 2-step nilpotent Lie groups | Closed timelike geodesies | Left-invariant Lorentz metrics | Physical Sciences | Mathematics | Science & Technology

Geometry | Mathematical theorems | Algebra | Nonexistence | Spacetime | Inner products | Lie groups | Mathematical vectors | Curvature | 2-step nilpotent Lie groups | Closed timelike geodesies | Left-invariant Lorentz metrics | Physical Sciences | Mathematics | Science & Technology

Journal Article

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