Results 241 to 250 of about 779 (266)
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The Scalar Curvature on Totally Geodesic Fiberings
Annals of Global Analysis and Geometry, 2000A compact Riemannian manifold \(N\) with scalar curvature \(\kappa _n\) is said to satisfy a comparison theorem for the scalar curvature iff for any other compact Riemannian manifold \(M\) (\(\dim M = \dim N\)) the inequality \(\kappa _M(x)\leq\kappa _N(f(x))\) holds at some \(x\in M\) whenever \(f:M\to N\) is a vector contracting spin map of non-zero ...
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Congruences of totally geodesic surfaces
Classical and Quantum Gravity, 1989A congruence of m-dimensional surfaces on a manifold M is a family of m- dimensional submanifolds which foliates M. Let (M,g) be a pseudo- Riemannian manifold. If every leaf is a totally geodesic submanifold, the congruence is said totally geodesic. The surface has rank k (\(\leq m)\) if at each point the induced ``metric'' has rank k.
Plebański, Jerzy F., Rózga, Krzysztof
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TOTALLY GEODESIC SURFACES AND QUADRATIC FORMS
Journal of Knot Theory and Its Ramifications, 2013Let M be a compact, connected, irreducible, orientable 3-manifold with torus boundary. A closed, orientable, immersed, incompressible surface F in M with no incompressible annulus joining F and ∂M compresses in at most finitely many Dehn fillings M(α).
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On totally geodesic affine immersions
Journal of Geometry, 1993The author studies totally geodesic affine immersions into manifolds of recurrent curvature. In particular he gives sufficient conditions for the projective flatness of the submanifold. Examples are given for the classes of submanifolds studied.
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Laplacian on a totally geodesic foliation
Journal of Geometry, 1997The work of \textit{L. Bérard-Bergery} and \textit{J.-P. Bourguignon} [Lect. Notes Math. 838, 30-35 (1981; Zbl 0437.53030)] on the Laplace-Beltrami operator acting on functions defined on the total space of a Riemannian submersion with totally geodesic fibers is extended to totally geodesic, bundle-like foliations \({\mathcal F}\) on a compact ...
Kang, Tae Ho +2 more
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Totally geodesic holomorphic subspaces
Nonlinear Analysis: Real World Applications, 2007The author studies totally geodesic holomorphic subspaces in a complex Finsler space with respect to a complex Berwald connection. The equations of the holomorphic subspace have simple expressions. The totally geodesic subspaces are characterized by using the second fundamental form of the complex Berwald connection.
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Total Scalar Curvatures of Geodesic Spheres and of Boundaries of Geodesic Disks
2007Total curvatures of boundaries of geodesic disks in Riemannian manifolds are investigated. The first terms in the corresponding power series expansions are obtained for the total scalar curvature and the L 2-norms of the scalar curvature, the Ricci tensor and the curvature tensor.
J. C. Díaz-Ramos +2 more
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Riemannian and Totally Geodesic Foliations
1988The transversal geometry of a foliation is the geometry infinitesimally modeled by Q, while the tangential geometry is infinitesimally modeled by L. A key fact is the existence of the Bott connection in Q defined by $$ {\mathop{\nabla }\limits^{^\circ }_{{{X^S}}}} = \pi [X,{Y_S}]\,{\text{for}}\,X \in \Gamma L,\,s \in \Gamma Q $$ (5.1) where ...
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The Totally Geodesic Coisotropic Submanifolds in Kähler Manifolds
Geometriae Dedicata, 2002A 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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A Totally Real Surface in CP 2 that is not Totally Geodesic
Proceedings of the American Mathematical Society, 1975Ludden, Gerald D. +2 more
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