The Lichnerowicz-Type Laplacians: Vanishing Theorems for Their Kernels and Estimate Theorems for Their Smallest Eigenvalues
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73627044" target="_blank" >RIV/61989592:15310/24:73627044 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/12/24/3936" target="_blank" >https://www.mdpi.com/2227-7390/12/24/3936</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math12243936" target="_blank" >10.3390/math12243936</a>
Alternative languages
Result language
angličtina
Original language name
The Lichnerowicz-Type Laplacians: Vanishing Theorems for Their Kernels and Estimate Theorems for Their Smallest Eigenvalues
Original language description
In the present paper, we prove several vanishing theorems for the kernel of the Lichnerowicz type Laplacian and provide estimates for its lowest eigenvalue on closed Riemannian manifolds. As an example of the Lichnerowicz-type Laplacian, we consider the Hodge–de Rham Laplacian acting on forms and ordinary Lichnerowicz Laplacian acting on symmetric tensors. Additionally, we prove vanishing theorems for the null spaces of these Laplacians and find estimates for their lowest eigenvalues on closed Riemannian manifolds with suitably bounded curvature operators of the first kind, sectional and Ricci curvatures. Specifically, we will prove our version of the famous differential sphere theorem, which we will apply to the forementioned problems concerning the ordinary Lichnerowicz Laplacian.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics
ISSN
2227-7390
e-ISSN
2227-7390
Volume of the periodical
12
Issue of the periodical within the volume
24
Country of publishing house
CH - SWITZERLAND
Number of pages
18
Pages from-to
"3936-1"-"3936-18"
UT code for WoS article
001384896600001
EID of the result in the Scopus database
2-s2.0-85213224506