Extrinsic homogeneity of parallel submanifolds II
نویسندگان
چکیده
منابع مشابه
On homogeneity of embedded submanifolds
We discuss in the paper the problem that is connected in their roots with the several variables complex analysis. But its study shows the actuality of the problem itself as well as the questins near to it for the many sections of modern mathematics, using or touching the notion of homogeneity. To exlain the interest of complex analysis to last term recall for example the classical Riemann theor...
متن کاملExtrinsic sphere and totally umbilical submanifolds in Finsler spaces
Based on a definition for circle in Finsler space, recently proposed by one of the present authors and Z. Shen, a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field, if and only if its circles coincide with circles of the ambient...
متن کاملHomogeneity of infinite dimensional isoparametric submanifolds
A subset S of a Riemannian manifoldN is called extrinsically homogeneous if S is an orbit of a subgroup of the isometry group of N . In [Th], Thorbergsson proved the remarkable result that every complete, connected, full, irreducible isoparametric submanifold of a finite dimensional Euclidean space of rank at least 3 is extrinsically homogeneous. This result, combined with results of [PT1] and ...
متن کاملOn the Extrinsic Topology of Lagrangian Submanifolds
We investigate the extrinsic topology of Lagrangian submanifolds and of their submanifolds in closed symplectic manifolds using Floer homological methods. The first result asserts that the homology class of a displaceable monotone Lagrangian submanifold vanishes in the homology of the ambient symplectic manifold. Combining this with spectral invariants we provide a new mechanism for proving Lag...
متن کاملPseudo-Parallel submanifolds
Pseudo-parallel (shortly PP) submanifolds are defined as a generalization of semi-parallel (shortly SP ) submanifolds and as extrinsic analogue of pseudo-symmetric (shortly PS) manifolds (in the sense of R. Deszcz) [1], [26]. Asperti et al [1] obtained a description of PP hypersurfaces in space form as quasiumbilic hypersurfaces or cyclids of Dupin and studied PP surfaces with maximal first nor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2011
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2010.12.008