Differential geometry of generalized 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...
متن کاملDifferential Geometry of Submanifolds of Projective Space: Rough Draft
• 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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Elements of noncommutative differential geometry of Z-graded generalized Weyl algebras A(p; q) over the ring of polynomials in two variables and their zero-degree subalgebras B(p; q), which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed. In particular, three classes of skew derivations of A(p; q) are constructed, and three-dimensional first-...
متن کاملGeneralized Complex Submanifolds
We introduce the notion of twisted generalized complex submanifolds and describe an equivalent characterization in terms of Poisson-Dirac submanifolds. Our characterization recovers a result of Vaisman [21]. An equivalent characterization is also given in terms of spinors. As a consequence, we show that the fixed locus of an involution preserving a twisted generalized complex structure is a twi...
متن کاملTrapped submanifolds in Lorentzian geometry
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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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2000
ISSN: 0030-8730
DOI: 10.2140/pjm.2000.194.285