On conformal diffeomorphisms of complete Riemannian manifolds with parallel Ricci tensor
نویسندگان
چکیده
منابع مشابه
Conformal mappings preserving the Einstein tensor of Weyl manifolds
In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...
متن کاملLocally conformal flat Riemannian manifolds with constant principal Ricci curvatures and locally conformal flat C-spaces
It is proved that every locally conformal flat Riemannian manifold all of whose Jacobi operators have constant eigenvalues along every geodesic is with constant principal Ricci curvatures. A local classification (up to an isometry) of locally conformal flat Riemannian manifold with constant Ricci eigenvalues is given in dimensions 4, 5, 6, 7 and 8. It is shown that any n-dimensional (4 ≤ n ≤ 8)...
متن کاملRicci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds
We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.
متن کاملAlmost Kenmotsu 3-h-manifolds with cyclic-parallel Ricci tensor
In this paper, we prove that the Ricci tensor of an almost Kenmotsu 3-h-manifold is cyclic-parallel if and only if it is parallel and hence, the manifold is locally isometric to either the hyperbolic space H3(−1) or the Riemannian product H2(−4)× R. c ©2016 All rights reserved.
متن کاملExistence of Complete Conformal Metrics of Negative Ricci Curvature on Manifolds with Boundary
We show that on a compact Riemannian manifold with boundary there exists u ∈ C(M) such that, u|∂M ≡ 0 and u solves the σk-Ricci problem. In the case k = n the metric has negative Ricci curvature. Furthermore, we show the existence of a complete conformally related metric on the interior solving the σk-Ricci problem. By adopting results of [14], we show an interesting relationship between the co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1971
ISSN: 0025-5645
DOI: 10.2969/jmsj/02310001