Complete 3d-Homogeneous Manifolds
نویسنده
چکیده
Assume that M is close three dimensional manifold. We prove that M \ {p} is a complete homogeneous manifold. As a corollary, we give a new proof on the classical Poincaré’s conjecture. Homogénéité variété de dimension trois Résumé. Soit M est une variété de dimension 3, conexe, fermée. Alors, M \{p} est complet Homogénéité variété. Nous présentons une neuve preuve du la Conjecture sur une variété de dimension trois de Poincaré.
منابع مشابه
ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE
A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...
متن کاملCOMPLETE k-CURVATURE HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS 0-MODELED ON AN INDECOMPOSIBLE SYMMETRIC SPACE
For k ≥ 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). The curvature tensor of these manifolds is modeled on that of an indecomposible symmetric space. All the local scalar Weyl curvature invariants of these manifolds vanish. Dedicated to Professor Sekigawa on his 60th bir...
متن کاملComplete k-Curvature Homogeneous Pseudo-Riemannian Manifolds
For k 2, we exhibit complete k-curvature homogeneous neutral signature pseudoRiemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). All the local scalar Weyl invariants of these manifolds vanish. These manifolds are Ricci flat, Osserman, and Ivanov–Petrova. Mathematics Subject Classification (2000): 53B20.
متن کاملFlat Homogeneous Pseudo-Riemannian Manifolds
The complete homogeneous pseudo-Riemannian manifolds of constant non-zero curvature were classified up to isometry in 1961 [1]. In the same year, a structure theory [2] was developed for complete fiat homogeneous pseudo-Riemannian manifolds. Here that structure theory is sharpened to a classification. This completes the classification of complete homogeneous pseudo-Riemannian manifolds of arbit...
متن کاملar X iv : m at h / 04 02 28 2 v 2 [ m at h . D G ] 5 A pr 2 00 4 COMPLETE CURVATURE HOMOGENEOUS PSEUDO - RIEMANNIAN MANIFOLDS
We exhibit 3 families of complete curvature homogeneous pseudo-Riemannian manifolds which are modeled on irreducible symmetric spaces and which are not locally homogeneous. All of the manifolds have nilpotent Jacobi operators; some of the manifolds are, in addition, Jordan Osserman and Jordan Ivanov-Petrova.
متن کامل