What is the Bochner Technique and Where is it Applied

In the present article we consider the generalized Bochner technique that is a natural development of the classical Bochner technique. As an illustration, we prove some Liouville-type theorems for Killing and Killing–Yano tensors, as well as for projective and conformal mappings of complete Riemanni...

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Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 43; no. 3; pp. 709 - 719
Main Authors Stepanov, S. E., Mikeš, J.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2022
Springer Nature B.V
Subjects
Algebra
Analysis
Conformal mapping
Geometry
Harmonic functions
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Riemann manifold
Tensors
Theorems
Liouville-type theorem
complete Riemannian manifold
Bochner technique
Killing and Killing–Yano tensors
projective and conformal mappings
subharmonic and superharmonic functions
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Summary:In the present article we consider the generalized Bochner technique that is a natural development of the classical Bochner technique. As an illustration, we prove some Liouville-type theorems for Killing and Killing–Yano tensors, as well as for projective and conformal mappings of complete Riemannian manifolds, using the -Liouville theorems for subharmonic and superharmonic functions.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080222060312