ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE

Document Type: research paper

Authors

Department of Mathematics, Faculty of Science, Imam Khomeini International University (IKIU), Qazvin, Iran.

Abstract

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds of nonpositive curvature states that a homogeneous Riemannian manifold  of nonpositive curvature is diffeomorphic to ...

Keywords


Article Title [Persian]

عمل گروه های ایزومتری نیم ساده روی برخی خمینه‌های ریمانی با خمیدگی نامثبت

Authors [Persian]

  • مرضیه بختیاری
  • رضا میرزایی
گروه ریاضی، دانشکده علوم پایه، دانشگاه بین المللی امام خمینی، قزوین، ایران
Abstract [Persian]

یک خمینه‌ همراه با عمل هموار گروه لی  G را G-خمینه می‌نامند. در این مقاله، خمینه‌ی ریمانی کامل M را همراه با عمل زیر گروه لی بسته G از ایزومتری‌ها در نظر می‌گیریم. بعد فضای مداری را نقص همگنی این عمل می‌نامند. خمینه‌هایی که عمل با نقص همگنی صفر دارند را همگن می‌نامند. قضیه‌ای در مورد خمینه‌های ریمانی با خمیدگی نامثبت بیان می‌کند که خمینه‌های همگن با خمیدگی نامثبت، با ...

Keywords [Persian]

  • خمینه‌های حاصلضربی
  • گروه لی نیم ساده
  • G-خمینه
  • نقص همگنی
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