Notes on conformal changes of Riemannian metrics
نویسندگان
چکیده
منابع مشابه
ON THE LIFTS OF SEMI-RIEMANNIAN METRICS
In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...
متن کاملOn conformal transformation of special curvature of Kropina metrics
An important class of Finsler metric is named Kropina metrics which is defined by Riemannian metric α and 1-form β which have many applications in physic, magnetic field and dynamic systems. In this paper, conformal transformations of χ-curvature and H-curvature of Kropina metrics are studied and the conditions that preserve this quantities are investigated. Also it is shown that in the ...
متن کاملSobolev Metrics on the Riemannian Manifold of All Riemannian Metrics
On the manifold M(M) of all Riemannian metrics on a compact manifold M one can consider the natural L-metric as decribed first by [10]. In this paper we consider variants of this metric which in general are of higher order. We derive the geodesic equations, we show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping. We give a condition...
متن کاملOn formal Riemannian metrics
Formal Riemannian metrics are characterized by the property that all products of harmonic forms are again harmonic. They have been studied over the last ten years and there are still many interesting open conjectures related to geometric formality. The existence of a formal metric implies Sullivan’s formality of the manifold, and hence formal metrics can exist only in presence of a very restric...
متن کاملOn geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1
The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new...
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: Kodai Mathematical Journal
سال: 1970
ISSN: 0386-5991
DOI: 10.2996/kmj/1138846223