Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Verdiani, Luigi"'
Autor:
Verdiani, Luigi, Ziller, Wolfgang
We study initial value problems for various geometric equations on a cohomogeneity manifold near a singular orbit. We show that when prescribing the Ricci curvature, or finding solutions to the Einstein and soliton equations, there exist solutions ne
Externí odkaz:
http://arxiv.org/abs/2412.06058
Autor:
Verdiani, Luigi, Ziller, Wolfgang
We classify complete curvature homogeneous metrics on simply connected four dimensional manifolds which are invariant under a cohomogeneity one action. We show that they are either isometric to a symmetric space with one of its cohomogeneity one acti
Externí odkaz:
http://arxiv.org/abs/2006.11294
Autor:
Verdiani, Luigi, Ziller, Wolfgang
In this paper we discuss the smoothness conditions for metrics on a cohomogeneity one manifold, i.e. metrics invariant under a Lie group whose generic orbits are hypersurfaces. Along these hypersurfaces one describes the metrics in terms of a collect
Externí odkaz:
http://arxiv.org/abs/1804.04680
Autor:
Verdiani, Luigi, Ziller, Wolfgang
We show that a certain family of cohomogeneity one manifolds does not admit an invariant metric of nonnegative sectional curvature, unless it admits one with positive curvature. As a consequence, the classification of nonnegatively curved cohomogenei
Externí odkaz:
http://arxiv.org/abs/1705.09032
Autor:
Verdiani, Luigi, Ziller, Wolfgang
Publikováno v:
J. Diff. Geom. 97 (2014) , 349-375
This is a significantly improved version with new applications. We show that there are many cohomogeneity one manifolds which do not admit an analytic invariant metric with non-negative sectional curvature, although they do have a smooth one. In part
Externí odkaz:
http://arxiv.org/abs/1012.2265
We construct a new 7-dimensional manifold with positive sectional curvature which is 2-connected with \pi_3=\Z_2 and admits an isometric group action with one dimensional quotient.
Comment: A few minor changes. To appear in GAFA
Comment: A few minor changes. To appear in GAFA
Externí odkaz:
http://arxiv.org/abs/0809.2304
Autor:
Verdiani, Luigi, Ziller, Wolfgang
We examine homogeneous metrics on spheres and determine which ones have positive sectional curvature. The answer is subtle and surprisingly difficult to prove. In some cases we also determine their pinching constants. This completes the classificatio
Externí odkaz:
http://arxiv.org/abs/0707.3056
Autor:
Podesta, Fabio, Verdiani, Luigi
We deal with seven dimensional compact Riemannian manifolds of positive curvature which admit a cohomogeneity one action by a compact Lie group G. We prove that the manifold is diffeomorphic to a sphere if the dimension of the semisimple part of G is
Externí odkaz:
http://arxiv.org/abs/dg-ga/9712002
Autor:
Podesta, Fabio, Verdiani, Luigi
We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved Riemannian manifolds which are acted on isometrically
Externí odkaz:
http://arxiv.org/abs/dg-ga/9711012
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