数学季刊 ›› 2004, Vol. 19 ›› Issue (4): 355-361.

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半对称度量循环联络的某些特征及曲率张量表示

  

  1. 1. Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China; 2. College of Mathematic and Information Science, Henan University , Kaifeng 475001, China
  • 收稿日期:2001-09-10 出版日期:2004-12-30 发布日期:2024-03-04
  • 作者简介:ZHAO Pei-biao(1964-),male,native of Huaiyuan,Anhui,an associate professor of Nanjing University of Science and Technology,Ph.D.,engages in differential geometry;SONG Hong-zao(1944-),male, native of Jiangyat,Jiangsu,a professor of Henan Universiy,engages in differential goometry;YNAG Xiao- ping(1962-),male,native of Hexian,Anhui,a professor of Nanjing University of Science and Technology,Ph.D., engages in nonlinear geometric analysis.
  • 基金资助:
     SupportedbyaGrant-in-idforScientificResearchfromNanjingUniversityofScienceandTechnologyandPartlybytheNNSF(19771048) SupportedbytheNNSF(19771048) SupportedbyaGrant-in-AidforScientificResearchfromHenanUniversity(200110475028)；

Some Invariant Properties of Semi-symmetric Metric Recurrent Connections and Curvature Tensor Expressions

  1. 1. Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China; 2. College of Mathematic and Information Science, Henan University , Kaifeng 475001, China
  • Received:2001-09-10 Online:2004-12-30 Published:2024-03-04
  • About author:ZHAO Pei-biao(1964-),male,native of Huaiyuan,Anhui,an associate professor of Nanjing University of Science and Technology,Ph.D.,engages in differential geometry;SONG Hong-zao(1944-),male, native of Jiangyat,Jiangsu,a professor of Henan Universiy,engages in differential goometry;YNAG Xiao- ping(1962-),male,native of Hexian,Anhui,a professor of Nanjing University of Science and Technology,Ph.D., engages in nonlinear geometric analysis.
  • Supported by:
     SupportedbyaGrant-in-idforScientificResearchfromNanjingUniversityofScienceandTechnologyandPartlybytheNNSF(19771048) SupportedbytheNNSF(19771048) SupportedbyaGrant-in-AidforScientificResearchfromHenanUniversity(200110475028)；

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摘要： The projective transformation of the special semi-symmetric metric recurrent connection is studied in this paper. First of all, an invariant under this transformation is granted; Secondly, by inducing of the invariant and making use of the properties that the corresponding covariant derivative keeps being fixed under the distinctness connection, the curvature tensor expression of the Riemannian manifold is posed at the same time.

关键词:  projective , transformation;semi-symmetric , metric , connection;metric , recurrent connection;invariant;curvature ,  tensor ,  , expression;covariant ,  , derivative

Abstract: The projective transformation of the special semi-symmetric metric recurrent connection is studied in this paper. First of all, an invariant under this transformation is granted; Secondly, by inducing of the invariant and making use of the properties that the corresponding covariant derivative keeps being fixed under the distinctness connection, the curvature tensor expression of the Riemannian manifold is posed at the same time.

Key words:  projective , transformation;semi-symmetric , metric , connection;metric , recurrent connection;invariant;curvature ,  tensor ,  , expression;covariant ,  , derivative

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