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Unit tangent bundle
About: Unit tangent bundle is a research topic. Over the lifetime, 1056 publications have been published within this topic receiving 15845 citations.
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TL;DR: In this paper, the authors studied the natural G2 structure on the unit tangent sphere bundle SM of any given orientable Riemannian 4-manifold M, as was discovered in Albuquerque and Salavessa (2009,2010) [9,10].
17 citations
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TL;DR: In this paper, it was shown that the pluriclosed flow preserves generalized Kahler structures with the extra condition $[J_+,J_-] = 0, a condition referred to as split tangent bundle.
Abstract: We show that the pluriclosed flow preserves generalized Kahler structures with the extra condition $[J_+,J_-] = 0$, a condition referred to as "split tangent bundle." Moreover, we show that in this in this case the flow reduces to a nonconvex fully nonlinear parabolic flow of a scalar potential function. We prove a number of a priori estimates for this equation, including a general estimate in dimension $n=2$ of Evans-Krylov type requiring a new argument due to the nonconvexity of the equation. The main result is a long time existence theorem for the flow in dimension $n=2$, covering most cases. We also show that the pluriclosed flow represents the parabolic analogue to an elliptic problem which is a very natural generalization of the Calabi conjecture to the setting of generalized Kahler geometry with split tangent bundle.
17 citations
TL;DR: In this paper, it was proved that a compact hypersurface in the Euclidean space with constant scalar curvature and nonnegative Ricci curvature is a sphere.
Abstract: Let M be a compact orientable submanifold immersed in a Riemannian manifold of constant curvature with flat normal bundle. This paper gives intrinsic conditions for M to be totally umbilical or a local product of several totally umbilical submanifolds. It is proved especially that a compact hypersurface in the Euclidean space with constant scalar curvature and nonnegative Ricci curvature is a sphere.
17 citations
TL;DR: In this article, the authors prove commutative integrability of the Hamilton system on the tangent bundle of the complex projective space whose Hamiltonian coincides with the Hamiltonian of the geodesic flow.
Abstract: We prove commutative integrability of the Hamilton system on the tangent bundle of the complex projective space whose Hamiltonian coincides with the Hamiltonian of the geodesic flow and the Poisson bracket deforms due to addition of the Fubini–Study form to the standard symplectic form.
17 citations
17 citations