Results 11 to 20 of about 214,617 (202)

A Classification of a Totally Umbilical Slant Submanifold of Cosymplectic Manifolds [PDF]

Abstract and Applied Analysis, 2012
We study slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold 𝑀 of a cosymplectic manifold 𝑀 is either an anti-invariant submanifold or a 1−dimensional submanifold.
Siraj Uddin, Cenap Ozel, Viqar Azam Khan
doaj   +2 more sources

On Totally Contact Umbilical Contact CR-Lightlike Submanifolds Of Indefinite Sasakian Manifolds

Demonstratio Mathematica, 2014
After brief introduction, we prove that a totally contact umbilical CR- lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold.
Gogna Manish, Kumar Rakesh, Nagaich R. K.   +2 more
doaj   +2 more sources

Totally geodesic submanifolds in exceptional symmetric spaces

Advances in Mathematics, 2023
We classify maximal totally geodesic submanifolds in exceptional symmetric spaces up to isometry. Moreover, we introduce an invariant for certain totally geodesic embeddings of semisimple symmetric spaces, which we call the Dynkin index. We prove a result analogous to the index conjecture: for every irreducible symmetric space of non-compact type ...
Kollross, Andreas, Rodríguez-Vázquez, Alberto   +1 more
openaire   +4 more sources

On Totally Geodesic Submanifolds

Axioms
We give a proof of Cartan’s Theorem on totally geodesic submanifolds for real analytic manifolds endowed with a real analytic, torsion-free, affine connection. We apply the theorem to real analytic Hadamard manifolds and, more generally, to real analytic manifolds with a torsion-free, analytic, affine connection, such that at a manifold point p∈M, the ...
Antonella Nannicini, Donato Pertici
openaire   +3 more sources

On the dimension of totally geodesic submanifolds in the Prym loci [PDF]

Bollettino dell'Unione Matematica Italiana, 2021
AbstractIn this paper we give a bound on the dimension of a totally geodesic submanifold of the moduli space of polarised abelian varieties of a given dimension, which is contained in the Prym locus of a (possibly) ramified double cover. This improves the already known bounds.
E. Colombo, P. Frediani
openaire   +4 more sources

A note on a totally umbilical proper slant submanifold of a nearly Kaehler manifold

Kuwait Journal of Science, 2013
In this paper, we study totally umbilical proper slant submanifolds of a nearly Kaehler manifold. We prove that every totally umbilical proper slant submanifold of a nearly Kaehler manifold is totally geodesic.  
KHUSHWANT SINGH, SIRAJ UDDIN, MERAJ ALI KHAN   +2 more
doaj   +1 more source

On Geodesic Triangles in Non-Euclidean Geometry [PDF]

Foundations
In this paper, we study centroids, orthocenters, circumcenters, and incenters of geodesic triangles in non-Euclidean geometry, and we discuss the existence of the Euler line in this context.
Antonella Nannicini, Donato Pertici
doaj   +2 more sources

Totally geodesic submanifolds of the complex quadric [PDF]

Differential Geometry and its Applications, 2008
In this article, relations between the root space decomposition of a Riemannian symmetric space of compact type and the root space decompositions of its totally geodesic submanifolds (symmetric subspaces) are described. These relations provide an approach to the classification of totally geodesic submanifolds in Riemannian symmetric spaces. In this way
Klein, Sebastian, Sebastian Klein
openaire   +3 more sources

Characterizations for totally geodesic submanifolds of a $ K $-paracontact manifold

AIMS Mathematics, 2021
The aim of the present paper is to study pseudoparallel invariant submanifolds of a K-paracontact metric manifold. We consider pseudoparallel, Ricci-generalized pseudoparallel and 2-Ricci generalized pseudo parallel invariant submanifolds of a K-paracontact manifold and we obtain new results.
Mert,Tuğba, Atçeken, Mehmet
openaire   +6 more sources

Hopf fibrations and totally geodesic submanifolds [PDF]

, 2023
We classify totally geodesic submanifolds in Hopf-Berger spheres, which constitute a special family of homogeneous spaces diffeomorphic to spheres constructed via Hopf fibrations.
Rodríguez-Vázquez, Alberto, Olmos, Carlos E.   +1 more
core   +1 more source