Geometries of homogeneous spaces
نویسنده
چکیده
θ. This definition is deficient as it depends on a choice of basis. A definition in R is that a rotation is a linear map g with an axis, a line L fixed by g, and on the orthogonal complement L⊥ of L the restriction of g is a two-dimensional rotation. For this to make sense, one must have understood that the two-dimensional definition is independent of basis, and that g does stabilize the orthogonal complement of any line fixed by it. Indeed, there is no necessity to refer to R. Any R vector space with an inner product works as well.
منابع مشابه
Critical points of the Black - Hole potential for homogeneous special geometries
We extend the analysis of N=2 extremal Black-Hole attractor equations to the case of special geometries based on homogeneous coset spaces. For non-BPS critical points (with non vanishing central charge) the (Bekenstein-Hawking) entropy formula is the same as for symmetric spaces, namely four times the square of the central charge evaluated at the critical point. For non homogeneous geometries t...
متن کاملGeometries of Orthogonal Groups and Their Contractions: a Unified Classical Deformation Viewpoint
The general aim of this paper is to describe a particular case of a classical scheme which involves a whole class of spaces, and geometries associated to a family of Lie groups. At all different levels of this scheme, either the spaces, the Lie groups or their Lie algebras are related among themselves by contractions, yet their properties can be dealt with in a completely unified way. The famil...
متن کاملQuantum symmetry groups of noncommutative spheres
We show that the noncommutative spheres of Connes and Landi are quantum homogeneous spaces for certain compact quantum groups. We give a general construction of homogeneous spaces which support noncommutative spin geometries.
متن کاملHereditarily Homogeneous Generalized Topological Spaces
In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$.
متن کامل2 O ct 2 01 1 GEOMETRY OF CURVES IN PARABOLIC HOMOGENEOUS SPACES
The current paper is devoted to the study of integral curves of constant type in parabolic homogeneous spaces. We construct a canonical moving frame bundle for such curves and give the criterium when it turns out to be a Cartan connection. Generalizations to parametrized curves, to higher-dimensional submanifolds and to general parabolic geometries are discussed.
متن کاملFrames and Homogeneous Spaces
Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...
متن کامل