The Lichnerowicz-Type Laplacians: Vanishing Theorems for Their Kernels and Estimate Theorems for Their Smallest Eigenvalues

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The Lichnerowicz-Type Laplacians: Vanishing Theorems for Their Kernels and Estimate Theorems for Their Smallest Eigenvalues

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The Lichnerowicz-Type Laplacians: Vanishing Theorems for Their Kernels and Estimate Theorems for Their Smallest Eigenvalues

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

2227-7390

Svazek periodika

12

Číslo periodika v rámci svazku

24

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

18

Strana od-do

"3936-1"-"3936-18"

Kód UT WoS článku

001384896600001

EID výsledku v databázi Scopus

2-s2.0-85213224506