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International Mathematics Research Notices, ISSN 1073-7928, 2015, Volume 2015, Issue 13, pp. 4901 - 4932
In this article, we classify expanding homogeneous Ricci solitons up to dimension 5, according to their presentation as homogeneous spaces. We obtain that they... 
MATHEMATICS | EINSTEIN SOLVMANIFOLDS | METRICS
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 10/2015, Volume 2015, Issue 707, pp. 217 - 245
In this paper we consider connections between Ricci solitons and Einstein metrics on homogeneous spaces. We show that a semi-algebraic Ricci soliton admits an... 
MATHEMATICS | CLASSIFICATION | SOLVMANIFOLDS
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 04/2019, Volume 199, Issue 1, pp. 373 - 397
Journal Article
Journal of Differential Geometry, ISSN 0022-040X, 2014, Volume 98, Issue 2, pp. 315 - 347
We bring new insights into the longstanding Alekseevskii conjecture, namely that any connected homogeneous Einstein manifold of negative scalar curvature is... 
MATHEMATICS | EINSTEIN SOLVMANIFOLDS | NILMANIFOLDS | SPACES
Journal Article
Communications in Analysis and Geometry, ISSN 1019-8385, 2011, Volume 19, Issue 5, pp. 831 - 854
We prove that the Ricci flow g(t) starting at any metric on R-n that is invariant by a transitive nilpotent Lie group N can be obtained by solving an ordinary... 
MATHEMATICS | EINSTEIN SOLVMANIFOLDS
Journal Article
Quarterly Journal of Mathematics, ISSN 0033-5606, 2014, Volume 65, Issue 2, pp. 399 - 419
We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space MATHEMATICS | SOLVMANIFOLDS | MANIFOLDS | NILMANIFOLDS | FLOW
Journal Article
Journal of the Korean Mathematical Society, ISSN 0304-9914, 2015, Volume 52, Issue 6, pp. 1209 - 1251
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2013, Volume 141, Issue 10, pp. 3651 - 3663
The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor... 
MATHEMATICS | GEOMETRIES | MATHEMATICS, APPLIED | CLASSIFICATION | EINSTEIN SOLVMANIFOLDS
Journal Article
Topology and its Applications, ISSN 0166-8641, 04/2016, Volume 202, pp. 397 - 409
The conjecture that every n-dimensional almost flat manifold (equivalently, infra-nilmanifold) is the boundary of an (n+1)-dimensional manifold has been long... 
Bounding problem | Infra-solvmanifolds | Involution | Solvmanifolds | Cobordism | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARIES | FLAT RIEMANNIAN-MANIFOLDS
Journal Article
Physical Review D - Particles, Fields, Gravitation and Cosmology, ISSN 1550-7998, 06/2011, Volume 83, Issue 12
A special class of Bianchi type I expanding solutions in a string motivated theory with a single scalar field has been speculated to break the cosmic no-hair... 
INSTABILITY | COSMOLOGICAL MODELS | BEHAVIOR | ASTRONOMY & ASTROPHYSICS | EINSTEIN SOLVMANIFOLDS | UNIVERSE | PHYSICS, PARTICLES & FIELDS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 08/2019, Volume 352, pp. 516 - 540
We show that for any solvable Lie group of real type, any homogeneous Ricci flow solution converges in Cheeger-Gromov topology to a unique non-flat... 
Ricci flow | Solvable Lie groups | Einstein solvmanifolds | MATHEMATICS | LONG-TIME BEHAVIOR | METRICS
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 02/2015, Volume 2015, Issue 699, pp. 159 - 182
In this work, we study metrics which are both homogeneous and Ricci soliton. If there exists a transitive solvable group of isometries on a Ricci soliton, we... 
MATHEMATICS | LIE-GROUPS | EINSTEIN | ISOMETRY GROUPS | METRICS | SOLVMANIFOLDS | MANIFOLDS | NILMANIFOLDS | FLOW
Journal Article
Izvestiya Mathematics, ISSN 1064-5632, 2017, Volume 81, Issue 6, pp. 1143 - 1154
We give an algebraic construction of extensions of arbitrary transitive actions of soluble Lie groups on compact manifolds. The question of the possible... 
Homogeneous space | Solvmanifold | Soluble Lie group | Lattice | Nilmanifold | MATHEMATICS | soluble Lie group | solvmanifold | lattice | SOLVMANIFOLDS | nilmanifold | homogeneous space | Questions | Group theory | Lie groups
Journal Article
Journal of Algebra, ISSN 0021-8693, 12/2017, Volume 491, pp. 474 - 489
We define a solvable extension of the graph 2-step nilpotent Lie algebras of [5] by adding elements corresponding to the 3-cliques of the graph. We study some... 
Graphs | Solvsolitons | Cliques | Solvable Lie algebras | MATHEMATICS | HOMOGENEOUS MANIFOLDS | 2-STEP | Lie algebras | CURVATURE | SOLVMANIFOLDS | Solvable | Algebra
Journal Article
Mathematische Annalen, ISSN 0025-5831, 06/2017, Volume 368, Issue 1-2, pp. 197 - 212
We refine existing structure results for non-compact, homogeneous, Einstein manifolds and provide a reduction in the classification problem of such spaces.... 
53C30 | 53C25 | MATHEMATICS | SPACES | CURVATURE | METRICS | REDUCTIVE GROUPS | SOLVMANIFOLDS | HOMOGENEOUS RICCI SOLITONS
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 6/2015, Volume 176, Issue 1, pp. 315 - 328
Infra-solvmanifolds are a certain class of aspherical manifolds which generalize both flat manifolds and almost flat manifolds (i.e., infra-nilmanifolds).... 
Geometry | 22E25 | Infra-solvmanifolds | 57S25 | 4 dimensional | Involution | Solvmanifolds | Cobordism | Primary 20H15 | Mathematics | 20F16 | 57R75 | MATHEMATICS | COBORDISM-CLASSES | FLAT RIEMANNIAN-MANIFOLDS
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 04/2017, Volume 114, pp. 581 - 586
Locally conformal Kähler manifold is said to be a Vaisman manifold if the Lee form is parallel with respect to the Riemannian metric. In this paper, we have... 
Solvmanifold | Locally conformal Kähler manifold | Vaisman manifold | MATHEMATICS, APPLIED | Locally conformal Kahler manifold | CONFORMAL KAHLER STRUCTURES | NILMANIFOLDS | PHYSICS, MATHEMATICAL | COMPACT SOLVMANIFOLDS
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 6/2018, Volume 289, Issue 1, pp. 605 - 628
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2017, Volume 369, Issue 4, pp. 2879 - 2896
Journal Article
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