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Award ID contains: 1654034

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  1. ; ; ; (, Differential Geometry and its Applications)
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  2. (, Letters in Mathematical Physics)
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  3. ; (, Differential Geometry and its Applications)
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  4. (, Advances in Geometry)
    Abstract In this paper, we classify the compact locally homogeneous non-gradient m -quasi Einstein 3- manifolds. Along the way, we also prove that given a compact quotient of a Lie group of any dimension that is m -quasi Einstein, the potential vector field X must be left invariant and Killing. We also classify the nontrivial m -quasi Einstein metrics that are a compact quotient of the product of two Einstein metrics. We also show that S 1 is the only compact manifold of any dimension which admits a metric which is nontrivially m -quasi Einstein and Einstein. 
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  5. (, Proceedings of the American Mathematical Society)
    In this paper, we generalize topological results known for noncompact manifolds with nonnegative Ricci curvature to spaces with nonnegative N N -Bakry Émery Ricci curvature. We study the Splitting Theorem and a property called the geodesic loops to infinity property in relation to spaces with nonnegative N N -Bakry Émery Ricci curvature. In addition, we show that if M n M^n is a complete, noncompact Riemannian manifold with nonnegative N N -Bakry Émery Ricci curvature where N > n N>n , then H n − 1 ( M , Z ) H_{n-1}(M,\mathbb {Z}) is 0 0 . 
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  6. (, Annals of Global Analysis and Geometry)
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  7. ; ; (, Letters in Mathematical Physics)
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  8. ; ; (, Calculus of Variations and Partial Differential Equations)
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  9. ; (, Journal of Geometry and Physics)
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  10. ; ; (, The Journal of Geometric Analysis)
    In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion-free connection introduced recently by the last two authors. We develop two new tools for studying weighted sectional curvature bounds: a new weighted Rauch comparison theorem and a modified notion of convexity for distance functions. As applications we prove generalizations of theorems of Preissman and Byers for negative curvature, the (homeomorphic) quarter-pinched sphere theorem, and Cheeger’s finiteness theorem. We also improve results of the first two authors for spaces of positive weighted sectional curvature and symmetry. 
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