Generalized Bochner technique and its application to the study of projective and conformal mappings

S. E. Stepanov ; J. Mikeš ; I. I. Tsyganok

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 112-122.

Résumé

In this paper, we consider the generalized Bochner technique, which is a natural development of the classical Bochner technique. As an illustration, we prove some vanishing theorems on Ricci solitons, conformal and projective mappings of complete Riemannian manifolds.

Détail

Mots-clés : Bochner technique, Ricci soliton
Keywords: complete Riemannian manifold, vanishing theorem, conformal mapping, projective mapping.

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