The existence of complete Riemannian metrics

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

Sobolev 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 کامل

On 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 کامل

Learning Riemannian Metrics

We consider the problem of learning a Riemannian metric associated with a given differentiable manifold and a set of points. Our approach to the problem involves choosing a metric from a parametric family that is based on maximizing the inverse volume of a given dataset of points. From a statistical perspective, it is related to maximum likelihood under a model that assigns probabilities invers...

متن کامل

Sobolev Metrics on the 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 described first by [11]. 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 conditio...

متن کامل

ذخیره 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: Proceedings of the American Mathematical Society

سال: 1961

ISSN: 0002-9939

DOI: 10.1090/s0002-9939-1961-0133785-8