Tsukuba Journal of Mathematics

A scalar Calabi-type flow in the almost Hermitian geometry

Masaya Kawamura

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We define a parabolic flow of almost Hermitian metrics which evolves an initial metric along the second derivative of the Chern scalar curvature. We show that the flow has a unique shorttime solution and also show a stability result when the background metric is quasi-Kähler with constant scalar curvature.

Article information

Tsukuba J. Math., Volume 43, Number 1 (2019), 37-54.

First available in Project Euclid: 25 October 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

almost Hermitian metric parabolic evolution equation Chern connection


Kawamura, Masaya. A scalar Calabi-type flow in the almost Hermitian geometry. Tsukuba J. Math. 43 (2019), no. 1, 37--54. doi:10.21099/tkbjm/1571968820. https://projecteuclid.org/euclid.tkbjm/1571968820

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