A holonomy proof of the positive curvature operator theorem

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

A geometric proof of the Berger Holonomy Theorem

We give a geometric proof of the Berger Holonomy Theorem. The proof uses Euclidean submanifold geometry of orbits and gives a link between Riemannian holonomy groups and normal holonomy groups.

متن کامل

A Theorem on Holonomy

Introduction. The object of this paper is to prove Theorem 2 of §2, which shows, for any connexion, how the curvature form generates the holonomy group. We believe this is an extension of a theorem stated without proof by E. Cartan [2, p. 4]. This theorem was proved after we had been informed of an unpublished related theorem of Chevalley and Koszul. We are indebted to S. S. Chern for many disc...

متن کامل

A New Proof of the Positive Energy Theorem*

A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau.) The relevance of these results to the stability of Minkowski space is discussed.

متن کامل

Sphere Theorem for Manifolds with Positive Curvature

In this paper, we prove that, for any integer n ≥ 2, there exists an ǫn ≥ 0 so that if M is an n-dimensional complete manifold with sectional curvature KM ≥ 1 and if M has conjugate radius bigger than π 2 and contains a geodesic loop of length 2(π − ǫn), then M is diffeomorphic to the Euclidian unit sphere S.

متن کامل

Another proof of Banaschewski's surjection theorem

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

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: 1980

ISSN: 0002-9939

DOI: 10.1090/s0002-9939-1980-0567991-7