New curvature conditions for Bochner techniques and applications: After Petersen and Wink

In this talk, we will review the recent works by Petersen and Wink regarding new curvature conditions for Bochner techniques on closed manifolds and its applications. Then, we continue there techniques to study non-compact complete manifolds and show several rigidity results of harmonic tensors in terms of Lichnerowicz Laplacians. Several applications to study geometry of curved manifolds and immersed submanifolds are also given .