خمينه هاي با مرتبه همگني يك و فضاهاي همگن با خميدگي اسكالر مثبت

Cohomogeneity One Manifolds an‎d Homogeneous Space of Positive Scalar Curvature

رياضي محض

This thesis examines cohomogeneity one manifolds an‎d homogeneous spaces of positive scalar curvature. Positive scalar curvature is one of the fundamental properties in Riemannian geometry, playing an important role in describing the geometric an‎d topological features of manifolds. In this thesis, we consider manifolds with compact Lie group actions whose orbit space is zero-or onediemensional, an‎d characterize such manifolds admitting positive scalar curvature.In addition, the impact of the symmetry group action an‎d characteristics of its orbits on the geometric structure of manifolds is analyzed. Another goal of this thesis is to provide new classifications an‎d a better understan‎ding of the behavior of these spaces under specific geometric conditions. Studying of these subjects not only helps to develop fundamental theories of differential geometry, but also it can be effective in applications related to theoretical physics.

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