Seminar GEOMETRIC ANALYSIS

Thời gian: 14:00 đến 16:30 ngày 11/06/2021, 14:00 đến 16:30 ngày 17/06/2021, 14:00 đến 16:30 ngày 24/06/2021, 14:00 đến 16:30 ngày 01/07/2021,

Địa điểm: C101, VIASM

Tóm tắt:
Date: Thursday, 1st July 2021
Time: 14h00- 16h30.
Speaker: Nguyen Thac Dung (VNU-University of Science, Hanoi)
Title: The first eigenvalue of Jacobi operator on hypersurfaces with constant mean curvature in spheres. 
Abstract: In this talk, we explain how to estimate the first eigenvalue of Jacobi operator on non-totally umbilical compact hypersurfaces (not need to be regular) with constant mean curvature in the unit sphere. Using this  estimate, we show new characterizations for certain Clifford tori. The talk is based on two papers by Chen and Cheng, and Jonathan Zhu in Calv. Var. 
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Date: Thursday, 24th June 2021
Time: 14h30- 16h30.
Speaker: Trần Thanh Hưng (Texas Tech University)
Title: The curvature operator of the second kind in dimension four. 
Abstract: In this talk, we explain how to determine the curvature of the second kind in dimension four. The key observation is that the product of two appropriate skew-symmetric matrices is a symmetric one. One application is to classify Einstein four-dimensional manifolds. The talk is based on a joint work with Matthew Gursky and Xiaodong Cao.
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Date:Thursday, 17th June 2021
Time: 14h30 - 16h30.
Speaker: Ha Tuan Dung (Hanoi Pedagogical University 2)
Title: On the curvature operator of the second kind (2nd talk).
Abstract: The aim of this talk is to study a similar problem in a Riemannian manifold of positive restricted curvature operator of the 2nd kind. We give a sufficient condition to ensure that a compact connected Riemannian manifold of positive restricted curvature operator of the 2nd kind is a space of constant curvature. We also point out that in an n-dimensional Riemannian manifold, the sectional curvature is positive if either the curvature operator of the 1st kind is positive; or the restricted curvature operator of the 2nd kind is positive. The talk is based on a paper by Kashiwada.
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Date: Friday, 11th June 2021
Time: 14h30 - 16h30.
Speaker: Ha Tuan Dung (Hanoi Pedagogical University 2)
Title: On the curvature operator of the second kind.
Abstract: The aim of this talk is to study a similar problem in a Riemannian manifold of positive restricted curvature operator of the 2nd kind. We give a sufficient condition to ensure that a compact connected Riemannian manifold of positive restricted curvature operator of the 2nd kind is a space of constant curvature. We also point out that in an n-dimensional Riemannian manifold, the sectional curvature is positive if either the curvature operator of the 1st kind is positive; or the restricted curvature operator of the 2nd kind is positive. The talk is based on a paper by Kashiwada.