ON THE CURVATURE OF THE FEFFERMAN METRIC OF CONTACT RIEMANNIAN MANIFOLDS

被引：2

作者：

Nagase, Masayoshi ^{[1
]}

机构：

[1] Saitama Univ, Grad Sch Sci & Engn, Dept Math, Saitama, Saitama 3388570, Japan

来源：

TOHOKU MATHEMATICAL JOURNAL | 2019年 / 71卷 / 03期

关键词：

Fefferman metric; scalar curvature; contact Riemannian structure; hermitian Tanno connection;

D O I：

10.2748/tmj/1568772179

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that a contact Riemannian manifold carries a generalized Fefferman metric on a circle bundle over the manifold. We compute the curvature of the metric explicitly in terms of a modified Tanno connection on the underlying manifold. In particular, we show that the scalar curvature descends to the pseudohermitian scalar curvature multiplied by a certain constant. This is an answer to a problem considered by Blair-Dragomir.

引用

页码：425 / 436

页数：12

共 50 条

[1] ALMOST CONTACT METRIC MANIFOLDS WITH SOME CONDITIONS FOR THE RIEMANNIAN CURVATURE TENSOR
ALEXIEV, VA
DOKLADI NA BOLGARSKATA AKADEMIYA NA NAUKITE, 1985, 38 (02): : 195 - 198
[2] Curvature of contact metric manifolds
Blair, DE
COMPLEX, CONTACT AND SYMMETRIC MANIFOLDS: IN HONOR OF L. VANHECKE, 2005, 234 : 1 - 13
[3] CURVATURE AND METRIC IN RIEMANNIAN 3-MANIFOLDS
NASU, T
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1975, 27 (02) : 194 - 206
[4] CURVATURE OF A RIEMANNIAN METRIC ON COMPACT HOMOGENEOUS MANIFOLDS
GORBATSEVICH, VV
MATHEMATICAL NOTES, 1988, 43 (1-2) : 95 - 99
[5] CONFORMAL CURVATURE OF CONTACT METRIC MANIFOLDS
Faraji, Hannane
Najafi, Behzad
Tabatabaeifar, Tayebeh
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2024, 39 (02): : 327 - 342
[6] On the curvature of a generalization of contact metric manifolds
Di Terlizzi, L
ACTA MATHEMATICA HUNGARICA, 2006, 110 (03) : 225 - 239
[7] CURVATURE OF A HYPERDISTRIBUTION AND CONTACT METRIC MANIFOLDS
SOLOVEV, AF
MATHEMATICAL NOTES, 1985, 38 (3-4) : 756 - 762
[8] On the curvature of a generalization of contact metric manifolds
Luigia Di Terlizzi
Acta Mathematica Hungarica, 2006, 110 : 225 - 239
[9] The curvature tensor of -contact metric manifolds
Arslan, Kadri
Carriazo, Alfonso
Martin-Molina, Veronica
Murathan, Cengizhan
MONATSHEFTE FUR MATHEMATIK, 2015, 177 (03): : 331 - 344
[10] Curvature identities for almost contact metric manifolds
E. A. Polkina
Russian Mathematics, 2007, 51 (7) : 54 - 57

← 1 2 3 4 5 →