Riemannian submanifolds
BY Chen - Handbook of differential geometry, 2000 - Elsevier
Problems in submanifold theory have been studied since the invention of calculus and it was
started with differential geometry of plane curves. Owing to his studies of how to draw …
started with differential geometry of plane curves. Owing to his studies of how to draw …
The geometry of homogeneous submanifolds of hyperbolic space
AJ Di Scala, C Olmos - Mathematische Zeitschrift, 2001 - Springer
We prove, in a purely geometric way, that there are no connected irreducible proper
subgroups of SO (N, 1). Moreover, a weakly irreducible subgroup of SO (N, 1) must either act …
subgroups of SO (N, 1). Moreover, a weakly irreducible subgroup of SO (N, 1) must either act …
Submanifolds with parallel mean curvature vector in Riemannian and indefinite space forms
BY Chen - arXiv preprint arXiv:1307.0430, 2013 - arxiv.org
A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature
vector if the mean curvature vector field H is parallel as a section of the normal bundle …
vector if the mean curvature vector field H is parallel as a section of the normal bundle …
Minimal homogeneous submanifolds in Euclidean spaces
AJ Di Scala - Annals of Global Analysis and Geometry, 2002 - Springer
Minimal Homogeneous Submanifolds in Euclidean Spaces Page 1 Annals of Global
Analysis and Geometry 21: 15–18, 2002. © 2002 Kluwer Academic Publishers. Printed in …
Analysis and Geometry 21: 15–18, 2002. © 2002 Kluwer Academic Publishers. Printed in …
Variationally complete representations are polar
A Di Scala, C Olmos - Proceedings of the American Mathematical Society, 2001 - ams.org
VARIATIONALLY COMPLETE REPRESENTATIONS ARE POLAR The concept of a variationally
complete action was introduced by R. Bott [B] in Page 1 PROCEEDINGS OF THE AMERICAN …
complete action was introduced by R. Bott [B] in Page 1 PROCEEDINGS OF THE AMERICAN …
[PDF][PDF] Holonomy and submanifold geometry
S Console, AJ Di Scala, C Olmos - ENSEIGNEMENT MATHEMATIQUE, 2002 - core.ac.uk
We survey applications of holonomic methods to the study of submanifold geometry,
showing the consequences of some sort of extrinsic version of de Rham decomposition and …
showing the consequences of some sort of extrinsic version of de Rham decomposition and …
A Berger type normal holonomy theorem for complex submanifolds
S Console, AJ Di Scala, C Olmos - Mathematische Annalen, 2011 - Springer
We prove a Berger type theorem for the normal holonomy Φ^ ⊥ (ie, the holonomy group of
the normal connection) of a full complete complex submanifold M of the complex projective …
the normal connection) of a full complete complex submanifold M of the complex projective …
Riemannian submanifolds: a survey
BY Chen - arXiv preprint arXiv:1307.1875, 2013 - arxiv.org
Submanifold theory is a very active vast research field which plays an important role in the
development of modern differential geometry. This branch of differential geometry is still so …
development of modern differential geometry. This branch of differential geometry is still so …
Submanifolds with curvature normals of constant length and the Gauss map
Let f: Mn! RN be a submanifold of euclidean space and let n0 Mfi be the maximal parallel
and flat subbundle of the normal bundle n Mfi. Then rankf Mfi is the dimension over M of …
and flat subbundle of the normal bundle n Mfi. Then rankf Mfi is the dimension over M of …