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Communications in Algebra, ISSN 0092-7872, 09/2018, Volume 46, Issue 9, pp. 4064 - 4078
The image of the higher Gauss map for a projective variety is discussed. The notion of higher Gauss maps here was introduced by Fyodor L. Zak as a... 
Veronese variety | dual variety | 14N05 | higher Gauss map | Boole's formula | degree bound | Maps | Images
Journal Article
Communications in Algebra, ISSN 0092-7872, 09/2018, Volume 46, Issue 9, pp. 4064 - 4078
Journal Article
by Kaji, H
COMMUNICATIONS IN ALGEBRA, ISSN 0092-7872, 2018, Volume 46, Issue 9, pp. 4064 - 4078
The image of the higher Gauss map for a projective variety is discussed. The notion of higher Gauss maps here was introduced by Fyodor L. Zak as a... 
MATHEMATICS | BUNDLES | Boole's formula | Veronese variety | dual variety | higher Gauss map | degree bound
Journal Article
Topology and its Applications, ISSN 0166-8641, 2012, Volume 159, Issue 2, pp. 537 - 544
We study the critical points of the normal map , where is an immersed -dimensional submanifold of , is the normal bundle of and if . Usually, the image of... 
Normal map | Strong principal directions | Focal set | Veronese of curvature | Critical points | Ellipse of curvature | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Topology and its Applications, ISSN 0166-8641, 02/2012, Volume 159, Issue 2, pp. 537 - 544
We study the critical points of the normal map ν:NM→R , where M is an immersed k-dimensional submanifold of R , NM is the normal bundle of M and ν(m, u)=m+u if... 
Normal map | Strong principal directions | Focal set | Veronese of curvature | Critical points | Ellipse of curvature
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 2012, Volume 62, Issue 1, pp. 124 - 136
We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations... 
Minkowski theorem | Discrete differential operators | Finite differences | Veronese maps | MATHEMATICS, APPLIED | DIFFUSION | PHYSICS, MATHEMATICAL
Journal Article
Journal of the Korean Mathematical Society, ISSN 0304-9914, 2007, Volume 44, Issue 2, pp. 407 - 442
The study of Euclidean submanifolds with finite type "classical" Gauss map was initiated by B.-Y. Chen and P. Piccinni in [11]. On the other hand, it was... 
Veronese surface | Spherical Gauss map | Equilateral torus | Finite type map | Clifford minimal torus | MATHEMATICS | spherical Gauss map | MATHEMATICS, APPLIED | MINIMAL IMMERSIONS | RULED SURFACES | finite type map | equilateral torus
Journal Article
Journal Article
by Vidal, R and Yi Ma and Sastry, S
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 12/2005, Volume 27, Issue 12, pp. 1945 - 1959
Journal Article
Topology and its Applications, ISSN 0166-8641, 02/2012, Volume 159, Issue 2, pp. 537 - 544
Journal Article
Annali di Matematica Pura ed Applicata, ISSN 0373-3114, 12/2017, Volume 196, Issue 6, pp. 2213 - 2237
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2019, Volume 371, Issue 4, pp. 2255 - 2278
Let SV^{\pmb n}_{\pmb d} be the Segre-Veronese variety given as the image of \mathbb{P}^{n_1}\times \dots \times \mathbb{P}^{n_r} under the embedding induced... 
secant varieties | MATHEMATICS | TENSORS | Segre-Veronese varieties | degenerations of rational maps | BI-DEGREE | secant defect | osculating spaces | SUMS
Journal Article
by Fei, J and He, L
ANNALI DI MATEMATICA PURA ED APPLICATA, ISSN 0373-3114, 12/2017, Volume 196, Issue 6, pp. 2213 - 2237
In this paper we determine all homogeneous minimal immersions of 2-spheres in quaternionic projective spaces . 
MATHEMATICS, APPLIED | HARMONIC MAPS | Veronese surfaces | PROJECTIVE SPACES | COMPLEX GRASSMANN MANIFOLD | Homogeneous harmonic maps | MATHEMATICS | Quaternionic projective spaces | Classification | CONSTRUCTION | CONSTANT CURVATURE | 2-SPHERES | S-2
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 07/2018, Volume 548, pp. 273 - 292
The Chow variety of polynomials that decompose as a product of linear forms has been studied for more than 100 years. Brill, Gordon and others obtained... 
[formula omitted]-module | Chow variety | Brill's equations | Brill's map | GL(V)-module | MATHEMATICS | PLETHYSM | MATHEMATICS, APPLIED | SEGRE VARIETIES | SECANT VARIETIES | VERONESE | IDEALS | Mathematical problems | Polynomials | Mapping | Algebraic group theory | Mathematical analysis | Linear algebra
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2014, Volume 83, Issue 287, pp. 1337 - 1372
Let U \subseteq H^0({\mathcal {O}_{\mathbb{P}^1 \times \mathbb{P}^1}}(2,1)) determine a regular map \phi _U: {\mathbb{P}^1 \times \mathbb{P}^1} \longrightarrow... 
Tensor product surface | Segre-Veronese map | Bihomogeneous ideal | BLOWING-UP RINGS | MATHEMATICS, APPLIED | APPROXIMATION COMPLEXES | HYPERSURFACES | bihomogeneous ideal | IMPLICITIZATION
Journal Article
Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 12/2017, Volume 196, Issue 6, pp. 2213 - 2237
In this paper we determine all homogeneous minimal immersions of 2-spheres in quaternionic projective spaces $${\mathbb {H}}P^n$$ H P n . 
Homogeneous harmonic maps | 53C42 | Veronese surfaces | Quaternionic projective spaces | 53C55 | Classification | Mathematics, general | Mathematics
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 02/2019, Volume 62, pp. 1 - 38
In this paper we completely classify the linearly full homogeneous holomorphic two-spheres in the complex Grassmann manifolds and . We also obtain the Gauss... 
The second fundamental form | Gaussian curvature | Veronese surfaces | Homogeneous holomorphic two-spheres | MATHEMATICS, APPLIED | HARMONIC MAPS | CURVES | MATHEMATICS | LIE-GROUPS | CLASSICAL-SOLUTIONS | CONSTRUCTION | RIGIDITY | CONSTANT CURVATURE | MINIMAL 2-SPHERES
Journal Article
Designs, Codes and Cryptography, ISSN 0925-1022, 12/2016, Volume 81, Issue 3, pp. 445 - 457
Journal Article
Computer Vision and Image Understanding, ISSN 1077-3142, 2006, Volume 103, Issue 3, pp. 208 - 217
In this paper, we study projection systems with a single effective viewpoint, including combinations of mirrors and lenses (catadioptric) as well as just... 
Catadioptrics | Lifting of coordinates | Radial distortion | Veronese maps | CALIBRATION | lifting of coordinates | veronese maps | radial distortion | catadioptrics | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Analysis | Algorithms
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 12/2015, Volume 43, pp. 21 - 44
In this paper, we firstly use Aithal's results to obtain some characterization of the harmonic sequence generated by linearly full non-degenerate holomorphic... 
Veronese curve | Holomorphic curve | Gauss curvature | Classification | Complex Grassmann manifold | MATHEMATICS | MATHEMATICS, APPLIED | HARMONIC MAPS | CONSTRUCTION | 2-SPHERES
Journal Article
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