Abstract:
In this talk, I will review the new curvature conditions given by Petersen and Wink in Bochner techniques. Then we use them to derive several vanishing and rigidity results on curved manifolds and immersed submanifolds.
References:
1. G. Colombo, M. Mariani, M. Rigoli, Tachibana-type theorems on complete manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. 25 (2024), no. 2, 1033-1083
2. G.H. Cho and N. T. Dung, Vanishing results from Lichnerowicz Laplacian on complete Kahler manifolds and application, Jour. Math. Anal. Appl., Volume 517, Issue 1 (2023), 126602
3. Gunhee Cho, N. T. Dung, and T. Q. Huy, Rigidity results with curvature conditions from Lichnerowicz Laplacian and applications, Preprint
4. N. T. Dung, Juncheol Pyo, and N. D. Tuyen, Vanishing results on weighted manifolds with lower bounds of the curvature operator, Submitted
5. P. Petersen and M. Wink, New Curvature Conditions for the Bochner Technique, Invent. Math. 224, 33-54 (2021)
6. P. Petersen and M. Wink, Vanishing and Estimation Results for Hodge numbers, Jour. Reine Angew. Math. 780 (2021), 197-219
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