Evolution for First Eigenvalue of L T,f on an Evolving Riemannian Manifold

Apurba Saha, Shahroud Azami, Daniel Breaz, Eleonora Rapeanu and Shyamal Kumar Hui ()
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Apurba Saha: Department of Mathematics, The University of Burdwan, Golapbag Campu, Burdwan 713104, India
Shahroud Azami: Department of Pure Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin 34148-96818, Iran
Daniel Breaz: Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
Eleonora Rapeanu: “Mircea cel Batran” Naval Academy, 900218 Constanta, Romania
Shyamal Kumar Hui: Department of Mathematics, The University of Burdwan, Golapbag Campu, Burdwan 713104, India

Mathematics, 2022, vol. 10, issue 23, 1-16

Abstract: In this paper, evolution formulas for the first non-zero eigenvalue of the operator L T , f on a weighted closed Riemannian manifold along the Ricci flow as well as along the Yamabe flow are formulated. Some monotonic quantities are also derived for the normalized Ricci flow on Bianchi classes.

Keywords: eigenvalue; Ricci flow; Yamabe flow; homogeneous 3-manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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