Lichnerowicz-Type Laplacians in the Bochner Technique

Vladimir Rovenski; Sergey Stepanov; Irina Tsyganok

doi:10.1007/978-3-031-50586-7_8

Lichnerowicz-Type Laplacians in the Bochner Technique

Vladimir Rovenski
, Sergey Stepanov
, Irina Tsyganok

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In the well-known monograph of A. Besse the following is written: the Bochner technique is a method of proving vanishing theorems for null space of a Laplace operator admitting a Weitzenböck decomposition and further of estimating its lowest nonzero eigenvalue. In this article, we consider a generalized form of the well-known Lichnerowicz Laplacian, show how the Bochner technique works for this operator and provide some its important examples.

Original language	English
Title of host publication	Differential Geometric Structures and Applications - 4th International Workshop on Differential Geometry, 2023
Editors	Vladimir Rovenski, Paweł Walczak, Robert Wolak
Publisher	Springer
Pages	167-207
Number of pages	41
ISBN (Print)	9783031505850
DOIs	https://doi.org/10.1007/978-3-031-50586-7_8
State	Published - 2024
Event	4th International Workshop on Differential Geometry, IWDG 2023 - Haifa, Israel Duration: 10 May 2023 → 13 May 2023

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	440
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	4th International Workshop on Differential Geometry, IWDG 2023
Country/Territory	Israel
City	Haifa
Period	10/05/23 → 13/05/23

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Keywords

53C21
58J05
Bochner technique
Lichnerowicz-type Laplacian
Riemannian manifold
Singular distribution
Weitzenböck decomposition formula

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-031-50586-7_8

Cite this

Rovenski, V., Stepanov, S., & Tsyganok, I. (2024). Lichnerowicz-Type Laplacians in the Bochner Technique. In V. Rovenski, P. Walczak, & R. Wolak (Eds.), Differential Geometric Structures and Applications - 4th International Workshop on Differential Geometry, 2023 (pp. 167-207). (Springer Proceedings in Mathematics and Statistics; Vol. 440). Springer. https://doi.org/10.1007/978-3-031-50586-7_8

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abstract = "In the well-known monograph of A. Besse the following is written: the Bochner technique is a method of proving vanishing theorems for null space of a Laplace operator admitting a Weitzenb{\"o}ck decomposition and further of estimating its lowest nonzero eigenvalue. In this article, we consider a generalized form of the well-known Lichnerowicz Laplacian, show how the Bochner technique works for this operator and provide some its important examples.",

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author = "Vladimir Rovenski and Sergey Stepanov and Irina Tsyganok",

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Rovenski, V, Stepanov, S & Tsyganok, I 2024, Lichnerowicz-Type Laplacians in the Bochner Technique. in V Rovenski, P Walczak & R Wolak (eds), Differential Geometric Structures and Applications - 4th International Workshop on Differential Geometry, 2023. Springer Proceedings in Mathematics and Statistics, vol. 440, Springer, pp. 167-207, 4th International Workshop on Differential Geometry, IWDG 2023, Haifa, Israel, 10/05/23. https://doi.org/10.1007/978-3-031-50586-7_8

Lichnerowicz-Type Laplacians in the Bochner Technique. / Rovenski, Vladimir; Stepanov, Sergey; Tsyganok, Irina.
Differential Geometric Structures and Applications - 4th International Workshop on Differential Geometry, 2023. ed. / Vladimir Rovenski; Paweł Walczak; Robert Wolak. Springer, 2024. p. 167-207 (Springer Proceedings in Mathematics and Statistics; Vol. 440).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024

Y1 - 2024

N2 - In the well-known monograph of A. Besse the following is written: the Bochner technique is a method of proving vanishing theorems for null space of a Laplace operator admitting a Weitzenböck decomposition and further of estimating its lowest nonzero eigenvalue. In this article, we consider a generalized form of the well-known Lichnerowicz Laplacian, show how the Bochner technique works for this operator and provide some its important examples.

AB - In the well-known monograph of A. Besse the following is written: the Bochner technique is a method of proving vanishing theorems for null space of a Laplace operator admitting a Weitzenböck decomposition and further of estimating its lowest nonzero eigenvalue. In this article, we consider a generalized form of the well-known Lichnerowicz Laplacian, show how the Bochner technique works for this operator and provide some its important examples.

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KW - 58J05

KW - Bochner technique

KW - Lichnerowicz-type Laplacian

KW - Riemannian manifold

KW - Singular distribution

KW - Weitzenböck decomposition formula

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A2 - Walczak, Paweł

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PB - Springer

T2 - 4th International Workshop on Differential Geometry, IWDG 2023

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ER -

Lichnerowicz-Type Laplacians in the Bochner Technique

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

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