On some $3$-dimensional complete Riemannian manifolds satisfying $R(X,\,Y)\cdot R=0$
نویسندگان
چکیده
منابع مشابه
Some Properties of Non-compact Complete Riemannian Manifolds
In this paper, we study the volume growth property of a non-compact complete Riemannian manifold X . We improve the volume growth theorem of Calabi (1975) and Yau (1976), Cheeger, Gromov and Taylor (1982). Then we use our new result to study gradient Ricci solitons. We also show that on X , for any q ∈ (0,∞), every non-negative L subharmonic function is constant under a natural decay condition ...
متن کاملQuasilinear elliptic inequalities on complete Riemannian manifolds
We prove maximum and comparison principles for weak distributional solutions of quasilinear, possibly singular or degenerate, elliptic differential inequalities in divergence form on complete Riemannian manifolds. A new definition of ellipticity for nonlinear operators on Riemannian manifolds is introduced, covering the standard important examples. As an application, uniqueness results for some...
متن کاملGauge Theories on Four Dimensional Riemannian Manifolds
This paper develops the Riemannian geometry of classical gauge theories Yang-Mills fields coupled with scalar and spinor fields on compact four-dimensional manifolds. Some important properties of these fields are derived from elliptic theory : regularity, an "energy gap theorem", the manifold structure of the configuration space, and a bound for the supremum of the field in terms of the energy....
متن کاملGeodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds
In this work it is shown that a necessary condition for the completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups, and not sufficient for 3-dimensional non unimodular Lie groups. As a consequence it is possible to identify, amongst the compact locally homogeneous Lorentzian 3-manifolds with n...
متن کاملComplete k-Curvature Homogeneous Pseudo-Riemannian Manifolds
For k 2, we exhibit complete k-curvature homogeneous neutral signature pseudoRiemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). All the local scalar Weyl invariants of these manifolds vanish. These manifolds are Ricci flat, Osserman, and Ivanov–Petrova. Mathematics Subject Classification (2000): 53B20.
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: Tohoku Mathematical Journal
سال: 1975
ISSN: 0040-8735
DOI: 10.2748/tmj/1178240942