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1.
In this article, we study the critical points of the total scalar curvature functional restricted to the space of metrics with constant scalar curvature of unitary volume, for simplicity, CPE metrics. Here, we prove that a CPE metric admitting a non-trivial closed conformal vector field must be isometric to a round sphere metric, which provides a partial answer to the CPE conjecture.  相似文献   

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We deal with a Riemannian manifoldM carrying a pair of skew symmetric conformal vector fields (X, Y). The existence of such a pairing is determined by an exterior differential system in involution (in the sense of Cartan). In this case,M is foliated by 3-dimensional totally geodesic submanifolds. Additional geometric properties are proved. Supported by a JSPS postdoctoral fellowship.  相似文献   

3.
We deal with a Riemannian manifoldM carrying a pair of skew symmetric conformal vector fields (X, Y). The existence of such a pairing is determined by an exterior differential system in involution (in the sense of Cartan). In this case,M is foliated by 3-dimensional totally geodesic submanifolds. Additional geometric properties are proved.  相似文献   

4.
Let be a closed, connected Riemannian manifold with a foliation of codimension q and a bundle-like metric g M . We study the relationship between several infinitesimal automorphisms. Moreover under the some curvature condition, if M admits a transversal conformal field, then is transversally isometric to the action of a finite subgroup of O(q) acting on the q-sphere of constant curvature.   相似文献   

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We give an estimate of the first lacuna in the distribution of mobility degrees r of n-dimensional (pseudo-)Riemannian spaces with respect to conformal mappings onto Einstein spaces. We obtain a tensor characteristic of spaces which are not conformally flat and have r = n − 1, which is the maximum possible value. Thus, we have found maximum mobile nonconformally flat spaces with r = n − 1.  相似文献   

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The flow on the Wiener space associated to a tangent process constructed by Cipriano and Cruzeiro, as well as by Gong and Zhang does not allow to recover Driver’s Cameron-Martin theorem on Riemannian path space. The purpose of this work is to refine the method of the modified Picard iteration used in the previous work by Gong and Zhang and to try to recapture and extend the result of Driver. In this paper, we establish the existence and uniqueness of a flow associated to a Cameron-Martin type vector field on the path space over a Riemannian manifold.  相似文献   

10.
A vector field on Riemannian manifold is called conformal Killing if it generates oneparameter group of conformal transformation. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometric and physical problems. In this paper, we prove that a trace-free conformal Killing tensor field is identically zero if it vanishes on some hypersurface. This statement is a basis of the theorem on decomposition of a symmetric tensor field on a compact manifold with boundary to a sum of three fields of special types. We also establish triviality of the space of trace-free conformal Killing tensor fields on some closed manifolds.  相似文献   

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Various concepts of invariant monotone vector fields on Riemannian manifolds are introduced. Some examples of invariant monotone vector fields are given. Several notions of invexities for functions on Riemannian manifolds are defined and their relations with invariant monotone vector fields are studied.  相似文献   

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In this paper,we study conformal vector fields on a Randers manifold with certain curvature properties.In particular,we completely determine conformal vector fields on a Randers manifold of weakly isotropic flag curvature.  相似文献   

15.
It is shown that if ann-dimensional (n≧3) Riemannian manifold admitsr≧2 locally symmetric vector fields (LSVF's), then it is aV(k)-space. In particular, ifr=n−1 then the manifold is a space of constant curvature. In the case of a 3-dimensional Riemannian manifold a close connection between LSVF's and eigenvectors of the Ricci tensor is found.  相似文献   

16.
We study pseudo-Riemannian conformal vector fields in the neighborhood of a singularity. For Riemannian manifolds, we prove that if a conformal vector field vanishing at a point x 0 is not Killing for a metric in the conformal class, then a neighborhood of the singularity x 0 is conformally flat.  相似文献   

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We show that the Dirac operator on a spin manifold does not admit L2 eigenspinors provided the metric has a certain asymptotic behaviour and is a warped product near infinity. These conditions on the metric are fulfilled in particular if the manifold is complete and carries a non-complete vector field which outside a compact set is gradient conformal and non-vanishing.  相似文献   

19.
In this paper, we construct an analogue of concircular fields for semi-Riemannian spaces (i.e., for manifolds with degenerate metrics). We find a tensor criterion of spaces admitting the maximal number of concircular fields or having no such fields. We detect a gap in the distribution of dimensions of the space of concircular fields, which, in contrast to the corresponding gap in the case of pseudo-Riemannian manifolds, is lesser by 1. We also study some special types of concircular fields having no analogues for pseudo-Riemannian manifolds. The canonical form of the metric for some classes of semi-Riemannian spaces admitting concircular fields is obtained. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 31, Geometry, 2005.  相似文献   

20.
Here, it is shown that every vector field on a Finsler space which keeps geodesic circles invariant is conformal. A necessary and sufficient condition for a vector field to keep geodesic circles invariant, known as concircular vector fields, is obtained. This leads to a significant definition of concircular vector fields on a Finsler space. Finally, complete Finsler spaces admitting a special conformal vector field are classified.  相似文献   

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