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Mat. Zametki, 2007, Volume 82, Issue 2, Pages 207–223 (Mi mz3790)  

This article is cited in 1 scientific paper (total in 1 paper)

$U(n+1)\times U(p+1)$-Hermitian Metrics on the Manifold $S^{2n+1}\times S^{2p+1}$

N. A. Daurtseva

Kemerovo State University

Abstract: A two-parameter family of invariant almost-complex structures $J_{a,c}$ is given on the homogeneous space $M\times M'=U(n+1)/U(n)\times U(p+1)/U(p)$; all these structures are integrable. We consider all invariant Riemannian metrics on the homogeneous space $M\times M'$. They depend on five parameters and are Hermitian with respect to some complex structure $J_{a,c}$. In this paper, we calculate the Ricci tensor, scalar curvature, and obtain estimates of the sectional curvature for any metric on $M\times M'$. All the invariant metrics of nonnegative curvature are described. We obtain the extremal values of the scalar curvature functional on the four-parameter family of metrics $g_{a,c,\lambda,\lambda';1}$.

Keywords: Hermitian metric on a homogenous space, Ricci tensor, sectional curvature, Hopf fibration, scalar curvature functional, holomorphic function, Lie algebra, Riemannian connection

DOI: https://doi.org/10.4213/mzm3790

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English version:
Mathematical Notes, 2007, 82:2, 180–195

Bibliographic databases:

UDC: 514.163
Received: 19.04.2004

Citation: N. A. Daurtseva, “$U(n+1)\times U(p+1)$-Hermitian Metrics on the Manifold $S^{2n+1}\times S^{2p+1}$”, Mat. Zametki, 82:2 (2007), 207–223; Math. Notes, 82:2 (2007), 180–195

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. N. A. Daurtseva, N. K. Smolentsev, “O pochti kompleksnykh strukturakh na shestimernykh proizvedeniyakh sfer”, Geometriya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 146, VINITI RAN, M., 2018, 17–47  mathnet  mathscinet
  • Математические заметки Mathematical Notes
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