Results 151 to 160 of about 217,631 (179)

Symplectomorphic codimension 1 totally geodesic submanifolds [PDF]

Differential Geometry and Its Applications, 1995
We show that the coisotropic totally geodesic properly embedded submanifolds of codimension 1 of a simply connected complete Kähler manifold of non-positive sectional curvature are symplectically linearizable. First we show that such a submanifold is foliated by totally geodesic complex leaves transversal to an isometric flow, hence, by a result of E ...
Ciriza, Eleonora
exaly   +3 more sources

Totally Geodesic Submanifolds and Polar Actions on Stiefel Manifolds

Journal of Geometric Analysis
We classify totally geodesic submanifolds of the real Stiefel manifolds of orthogonal two-frames. We also classify polar actions on these Stiefel manifolds, specifically, we prove that the orbits of polar actions are lifts of polar actions on the corresponding Grassmannian. In the case of cohomogeneity-one actions we are able to obtain a classification
Claudio Gorodski, Alberto Rodriguez-Vazquez   +1 more
exaly   +6 more sources

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TOTALLY GEODESIC SUBMANIFOLDS OF GL-MANIFOLDS

International Journal of Geometric Methods in Modern Physics, 2012
In this paper, for a Finsler manifold (M, F) with a Finsler metric gij(x, y) we shall consider a generalized Lagrange metrics (FGL-metrics) as the form *gij(x, y) = gij(x, y) + σ(x, y)Bi(x, y)Bj(x, y) on TM. Then we shall consider a Riemannian manifold (TM, *G) in which *G is a generalized Sasakian metric of *g on [Formula: see text]. Then we restrict
Laleh, Abolghasem, Rezaii, Morteza M., Hushmandi, Ataabak Baagherzadeh   +2 more
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Random 3-manifolds have no totally geodesic submanifolds

Annals of Global Analysis and Geometry
Abstract Murphy and the second author showed that a generic closed Riemannian manifold has no totally geodesic submanifolds, provided the ambient space is at least four dimensional. Lytchak and Petrunin established a similar result in dimension 3. For the higher dimensional result, the “generic set” is open and dense in the
Frederick Wilhelm, Wilhelm Frederick
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A Practical Criterion For Some Submanifolds To Be Totally Geodesic

Monatshefte für Mathematik, 2006
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Kim, Young Ho, Maeda, Sadahiro
openaire   +2 more sources

Totally geodesic submanifolds in Lie groups

Acta Mathematica Hungarica, 2006
We study minimal and totally geodesic submanifolds in Lie groups and related problems. We show that: (1) The imbedding of the Grassmann manifold G F (n,N) in the Lie group G F (N) defined naturally makes G F (n,
exaly   +2 more sources

Submanifolds with totally geodesic Gauss image

Geometriae Dedicata, 1984
This is a continuation for higher dimensions of the author's paper [Indiana Univ. Math. J. 32, 143-154 (1983; Zbl 0471.53004]. Beyond the property of totally geodesic Gauss map (into the Grassmannian) additional assumptions like ''conformal Gauss map'' or ''flat normal connection'' are needed to obtain significant consequences.
Chen, Bang-Yen, Yamaguchi, Seiichi
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The volume of geodesic balls and tubes about totally geodesic submanifolds in compact symmetric spaces [PDF]

Differential Geometry and Its Applications, 1997
Let M be a compact Riemannian symmetric space. We give an analytical expression for the area and volume functions of geodesic balls in M and for the area and volume functions of tubes around some totally geodesic submanifolds P of M.
Naveira, A.M., Gual, X.
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The Totally Geodesic Coisotropic Submanifolds in Kähler Manifolds

Geometriae Dedicata, 2002
A real submanifold \(\Sigma\) in a symplectic manifold \((M^{2n}, \omega)\) is said to be a coisotropic submanifold if \(T_p\Sigma^\omega \subset T_p\Sigma\) for all \(p\in\Sigma\), where \(T_p\Sigma^\omega= \{X\in T_pM\mid \omega (X,Y)=0\), \(\forall Y\subset T_p\Sigma\}\) is the symplectic complement of \(T_p \Sigma\).
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Isometric mappings and totally geodesic submanifolds of Finsler manifolds

Periodica Mathematica Hungarica
Rongmu Yan
exaly   +2 more sources