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Abstract
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We discuss a new relationship between the conformal vector field and the
-scalar curvature for
general
on a closed
manifold. The case
is well known and has been widely used. Several applications of the identities derived
for the general case are given.
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Keywords
conformal vector field, $\sigma_k$-scalar curvature,
maximum principle, Ricci curvature, locally conformally
flat
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Mathematical Subject Classification
Primary: 58J60
Secondary: 58J05
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Milestones
Received: 9 March 2021
Revised: 28 September 2021
Accepted: 4 December 2021
Published: 6 April 2022
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