Conformally flat hypersurfaces of symmetric spaces
نویسندگان
چکیده
منابع مشابه
Kaluza-klein Reduction of Conformally Flat Spaces
A “conformal tensor” is constructed from the metric tensor gMN (or Vielbein e A M ) and is invariant against Weyl rescaling gMN → egMN (or eM → eeM ). Moreover, it vanishes if and only if the space is conformally flat, gMN = e ηMN (or e A M = eδ M ). In dimension four or greater the conformal tensor is the Weyl tensor. In three dimensions the Weyl tensor vanishes identically, while the Cotton t...
متن کاملConformally Flat Spherically Symmetric Cosmological Models-revisited
Conformally flat spherically symmetric cosmological models representing a charged perfect fluid as well as a bulk viscous fluid distribution have been obtained. The cosmological constant Λ is found positive and is a decreasing function of time which is consistent with the recent supernovae observations. The physical and geometrical properties of the models are discussed.
متن کاملThe Symmetry Group of Lamé’s System and the Associated Guichard Nets for Conformally Flat Hypersurfaces
We consider conformally flat hypersurfaces in four dimensional space forms with their associated Guichard nets and Lamé’s system of equations. We show that the symmetry group of the Lamé’s system, satisfying Guichard condition, is given by translations and dilations in the independent variables and dilations in the dependents variables. We obtain the solutions which are invariant under the acti...
متن کاملClosed Hypersurfaces of Prescribed Mean Curvature in Locally Conformally Flat Riemannian Manifolds
We prove the existence of smooth closed hypersurfaces of prescribed mean curvature homeomorphic to S for small n, n ≤ 6, provided there are barriers. 0. Introduction In a complete (n+1)-dimensional manifold N we want to find closed hypersurfaces M of prescribed mean curvature. To be more precise, let Ω be a connected open subset of N , f ∈ C(Ω̄), then we look for a closed hypersurface M ⊂ Ω such...
متن کاملOn Totally Umbilical Hypersurfaces of Weakly Projective Symmetric Spaces
The object of the present paper is to study the totally umbilical hypersurfaces of weakly projective symmetric spaces and it is shown that the totally umbilical hypersurfaces of weakly projective symmetric space is also a weakly projective symmetric space.
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: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1985
ISSN: 0263-6115
DOI: 10.1017/s1446788700023065