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1.
We study the geometry of orthonormal frame bundles OM over Riemannian manifolds (M, g). The former are equipped with some modifications of the Sasaki-Mok metric depending on one real parameter c ≠ 0. The metrics are “strongly invariant” in some special sense. In particular, we consider the case when (M, g) is a space of constant sectional curvature K. Then, for dim M > 2, we find always, among the metrics , two strongly invariant Einstein metrics on OM which are Riemannian for K > 0 and pseudo-Riemannian for K < 0. At least one of them is not locally symmetric. We also find, for dim M ≥ 2, two invariant metrics with vanishing scalar curvature.
相似文献
2.
Let (M, g) be a compact oriented four-dimensional Einstein manifold. If M has positive intersection form and g has non-negative sectional curvature, we show that, up to rescaling and isometry, (M, g) is 2, with its standard Fubini–Study metric. 相似文献
3.
J. Kim 《Siberian Mathematical Journal》2006,47(1):64-67
We show that every compact Einstein Hermitian surface with constant conformal scalar curvature is a Kahler surface and that, in contrast to the compact case, there exits a noncompact Einstein Hermitian and non-Kahler surface with constant conformal scalar curvature. 相似文献
4.
Yu. G. Nikonorov 《Siberian Advances in Mathematics》2007,17(3):153-170
The main result of the article is as follows: If a nilpotent noncommutative metric Lie algebra (n, Q) is such that the operator Id ? trace(Ric) / trace(Ric2) Ric is positive definite then every Einstein solvable extension of (n, Q) is standard. We deduce several consequences of this assertion. In particular, we prove that all Einstein solvmanifolds of dimension at most 7 are standard. 相似文献
5.
This paper is devoted to the classification of seven-dimensional homogeneous Einstein manifolds with positive scalar curvature.Mathematics Subject Classifications (2000). 53C25, 53C30.The author was supported by RFBR (codes 02-01-01071, 01-01-06224, 00-15-96165). 相似文献
6.
Einstein metrics are solutions to Einstein field equation in General Relativity containing the Ricci-flat metrics. Einstein Finsler metrics which represent a non-Riemannian stage for the extensions of metric gravity, provide an interesting source of geometric issues and the (α,β)-metric is an important class of Finsler metrics appearing iteratively in physical studies. It is proved that every n-dimensional (n≥3) Einstein Matsumoto metric is a Ricci-flat metric with vanishing S-curvature. The main result can be regarded as a second Schur type Lemma for Matsumoto metrics. 相似文献
7.
In this work, it is proved that if a complete Finsler manifold of positive constant Ricci curvature admits a solution to a certain ODE, then it is homeomorphic to the n-sphere. Next, a geometric meaning is obtained for solutions of this ODE, which is applicable to Einstein–Randers spaces. Moreover, some results on Finsler spaces admitting a special conformal vector field are obtained. 相似文献
8.
Noncompact Homogeneous Einstein 5-Manifolds 总被引:1,自引:0,他引:1
This article is devoted to the classification of noncompact homogeneous Einstein 5-manifolds. In particular, we prove that each noncompact homogeneous Einstein 5-manifolds is locally isometric to some standard Einstein solvmanifoldMathematics Subject Classifications (2000). 53C25, 53C30 相似文献
9.
J. Heber 《Geometric And Functional Analysis》2006,16(4):869-890
We classify noncompact homogeneous spaces which are Einstein and asymptotically harmonic. This completes the classification of Riemannian harmonic spaces in the homogeneous case: Any simply connected homogeneous harmonic space is flat, or rank-one symmetric, or a nonsymmetric
Damek–Ricci space. Independently, Y. Nikolayevsky has obtained the latter classification under the additional assumption of
nonpositive sectional curvatures [N2].
Supported in part by DFG priority program “Global Differential Geometry” (SPP 1154).
Received: September 2004; Revision: June 2005; Accepted: September 2005 相似文献
10.
Mohammed-Larbi Labbi 《Annals of Global Analysis and Geometry》1997,15(4):299-312
We establish the stability of the class of manifolds with positive p-curvature under surgeries in codimension p + 3. As a consequence of this result, we first obtain the classification of compact 2-connected manifolds of dimension 7 with positive Einstein tensor; and secondly the existence of metrics with positive Einstein tensor on any compact, simply connected, non-spin manifold of dimension 7 whose second homotopy group is isomorphic to Z2. 相似文献
11.
By introducing the notion of single colored Finsler manifold, we deduce the curvature formulas of a homogeneous Finsler space. It results in a set of fundamental equations that are more elegant than the Riemannian case. Several applications of the equations are also supplied. 相似文献
12.
Bing Ye Wu 《Journal of Mathematical Analysis and Applications》2010,372(1):244-251
We investigate the spacelike hypersurfaces in Lorentzian space forms (n?4) with two distinct non-simple principal curvatures without the assumption that the (high order) mean curvature is constant. We prove that any spacelike hypersurface in Lorentzian space forms with two distinct non-simple principal curvatures is locally conformal to the Riemannian product of two constant curved manifolds. We also obtain some characterizations for hyperbolic cylinders in Lorentzian space forms in terms of the trace free part of the second fundamental form. 相似文献
13.
We construct new homogeneous Einstein spaces with negativeRicci curvature in two ways: First, we give a method for classifying andconstructing a class of rank one Einstein solvmanifolds whose derivedalgebras are two-step nilpotent. As an application, we describe anexplicit continuous family of ten-dimensional Einstein manifolds with atwo-dimensional parameter space, including a continuous subfamily ofmanifolds with negative sectional curvature. Secondly, we obtain newexamples of non-symmetric Einstein solvmanifolds by modifying thealgebraic structure of non-compact irreducible symmetric spaces of rankgreater than one, preserving the (constant) Ricci curvature. 相似文献
14.
15.
We classify positively curved self-dual Einstein Hermitian orbifold metrics of Galicki – Lawson on the weighted projective
planes. We thus determine which of the 3-Sasakian S1-reductions of S11 possess canonical variation metrics of positive sectional curvature.
Mathematics Subject Classifications (2000): 53C21, 53C25, 53C26 相似文献
16.
Heberto del Rio Guerra 《Annals of Global Analysis and Geometry》2002,21(4):319-339
We study the behavior of the moduli space of solutions to theSeiberg–Witten equations under a conformal change in the metric of aKähler surface (M,g). If the canonical line bundle K
M is ofpositive degree, we prove there is only one (up to gauge) solution tothe equations associated to any conformal metric to g. We use this, toconstruct examples of four dimensional manifolds withSpin
c
-structures, whose moduli spaces of solutions to theSeiberg–Witten equations, represent a nontrivial bordism class ofpositive dimension, i.e. the Spin
c
-structures are not inducedby almost complex structures. As an application, we show the existenceof infinitely many nonhomeomorphic compact oriented 4-manifolds withfree fundamental group and predetermined Euler characteristic andsignature that do not carry Einstein metrics. 相似文献
17.
We study a special class of Finsler metrics,namely,Matsumoto metrics F=α2α-β,whereαis a Riemannian metric andβis a 1-form on a manifold M.We prove that F is a(weak)Einstein metric if and only ifαis Ricci flat andβis a parallel 1-form with respect toα.In this case,F is Ricci flat and Berwaldian.As an application,we determine the local structure and prove the 3-dimensional rigidity theorem for a(weak)Einstein Matsumoto metric. 相似文献
18.
Yuri Nikolayevsky 《Geometriae Dedicata》2008,135(1):87-102
The structure of a solvable Lie group admitting an Einstein left-invariant metric is, in a sense, completely determined by the nilradical of its Lie algebra. We give an easy-to-check necessary and sufficient condition for a nilpotent algebra to be an Einstein nilradical whose Einstein derivation has simple eigenvalues. As an application, we classify filiform Einstein nilradicals (modulo known classification results on filiform graded Lie algebras). 相似文献
19.
In this paper, we investigate complete curvature-adapted submanifolds with maximal flat section and trivial normal holonomy group in symmetric spaces of compact type or non-compact type under a certain condition, and derive the constancy of the principal curvatures of such submanifolds. As a result, we derive that such submanifolds are isoparametric. 相似文献
20.
MARTIN LANZENDORF 《Geometriae Dedicata》1997,66(2):187-202
The purpose of this article is to study some simply connected Lie groups with left invariant Einstein metric, negative Einstein constant and nonpositive sectional curvature. These Lie groups are classified if their associated metric Lie algebra s is of Iwasawa type and s = An1n2...nr, where all niare Lie algebras of Heisenberg type with [[ni,nj] = {0} for ij. The most important ideas of the article are based on a construction method for Einstein spaces introduced by Wolter in 1991. By this method some new examples of Einstein spaces with nonpositive curvature are constructed. In another part of the article it is shown that Damek-Ricci spaces have negative sectional curvature if and only if they are symmetric spaces. 相似文献