排序方式: 共有15条查询结果,搜索用时 15 毫秒
1.
J. Carlos Díaz-Ramos Ramón Vázquez-Lorenzo 《Differential Geometry and its Applications》2006,24(4):433-442
Explicit examples of Osserman 4-manifolds with exactly two distinct eigenvalues of the Jacobi operators, α and β=4α≠0, are given. The former has multiplicity two and is a double root of the minimal polynomial of the Jacobi operators. 相似文献
2.
J. Carlos Díaz-Ramos Eduardo García-Río Luis Hervella 《Annali di Matematica Pura ed Applicata》2005,184(1):115-130
Total scalar curvatures of geodesic spheres obtained by integrating the second-order scalar invariants of the curvature tensor are investigated. The first terms in their power-series expansions are derived and these results are used to characterize the two-point homogeneous spaces among Riemannian manifolds with adapted holonomy. Dedicated to Professor L. VanheckeMathematics Subject Classification (2000) 53C25, 53C30 相似文献
3.
J. Carlos Díaz-Ramos Eduardo García-Río Lieven Vanhecke 《Monatshefte für Mathematik》2006,184(1):303-322
We study some scalar curvature invariants on geodesic spheres and use them to characterize several kinds of Riemannian manifolds
such as homogenous manifolds and in particular, the two-point homogeneous spaces and the Damek-Ricci spaces. 相似文献
4.
Volume comparison results are obtained for the volume of geodesic celestial spheres in Lorentzian manifolds and the corresponding objects in Lorentzian space forms. Also, as a rigidity result it is shown that the volume of geodesic celestial spheres is independent of the instantaneous observer if and only if the spacetime has constant curvature. 相似文献
5.
José Carlos Díaz-Ramos Miguel Domínguez-Vázquez Cristina Vidal-Castiñeira 《Annals of Global Analysis and Geometry》2018,53(2):205-216
We show that an isoparametric submanifold of a complex hyperbolic plane, according to the definition of Heintze, Liu and Olmos’, is an open part of a principal orbit of a polar action. We also show that there exists a non-isoparametric submanifold of the complex hyperbolic plane that is isoparametric according to the definition of Terng’s. Finally, we classify Terng-isoparametric submanifolds of two-dimensional complex space forms. 相似文献
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We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide
a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the
homogeneous hypersurfaces together with their multiplicities.
相似文献
8.
Alexandre Cortés-Ayaso J. Carlos Díaz-Ramos Eduardo García-Río 《Annals of Global Analysis and Geometry》2008,34(2):185-193
It is shown that any four-dimensional Walker metric of nowhere zero scalar curvature has a natural almost para-Hermitian structure.
In contrast to the Goldberg–Sachs theorem, if this structure is self-dual and *-Einstein, it is symplectic but not necessarily
integrable. This is due to the non-diagonalizability of the self-dual Weyl conformal curvature tensor.
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We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar and the section is the tangent space of an embedded totally geodesic submanifold. We apply this to obtain a classification of polar actions with a fixed point on symmetric spaces. 相似文献