Differential Geometry of Rectifying Submanifolds
نویسندگان
چکیده
منابع مشابه
Differential Geometry of Submanifolds of Projective Space
These are lecture notes on the rigidity of submanifolds of projective space “resembling” compact Hermitian symmetric spaces in their homogeneous embeddings. The results of [16, 20, 29, 18, 19, 10, 31] are surveyed, along with their classical predecessors. The notes include an introduction to moving frames in projective geometry, an exposition of the Hwang-Yamaguchi ridgidity theorem and a new v...
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• Introduction to the local differential geometry of submanifolds of projective space • Introduction to moving frames for projective geometry • How much must a submanifold X ⊂ PN resemble a given submanifold Z ⊂ PM infinitesimally before we can conclude X ≃ Z? • To what order must a line field on a submanifold X ⊂ PN have contact with X before we can conclude the lines are contained in X? • App...
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In Lorentzian geometry, the concept of trapped submanifold is introduced by means of the mean curvature vector properties. Trapped submanifolds are generalizations of the standard maximal hypersurfaces and minimal surfaces, of geodesics, and also of the trapped surfaces introduced by Penrose. Selected applications to gravitational theories are mentioned.
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We prove explicit upper and lower bounds for the torsional rigidity of extrinsic domains of submanifolds P with controlled radial mean curvature in ambient Riemannian manifolds N with a pole p and with sectional curvatures bounded from above and from below, respectively. These bounds are given in terms of the torsional rigidities of corresponding Schwarz symmetrizations of the domains in warped...
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This article grew out of several talks that the author presented at the Banach Institute and at the University of Bialystok in Poland during November of 2001. It describes six problems from the geometry of submanifolds. Some of the problems come from the theory of constant curvature submanifolds in Euclidean space, as well as applications of Morse theory of the height function to the problem of...
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ژورنال
عنوان ژورنال: International Electronic Journal of Geometry
سال: 2016
ISSN: 1307-5624
DOI: 10.36890/iejg.584566