延边大学学报(自然科学版)
延邊大學學報(自然科學版)
연변대학학보(자연과학판)
JOURNAL OF YANBIAN UNIVERSITY(NATURAL SCIENCE EDITION)
2014年
4期
290-294
,共5页
半对称射影共形联络%半对称射影联络%半对称共形联络%常曲率
半對稱射影共形聯絡%半對稱射影聯絡%半對稱共形聯絡%常麯率
반대칭사영공형련락%반대칭사영련락%반대칭공형련락%상곡솔
semi-symmetric proj ective conformal connection%semi-symmetric proj ective connection%semi-symmetric conformal connection%constant curvature
在黎曼流形上定义了一个半对称射影共形联络,并研究了其性质,同时指出这种联络在特殊情形下可成半对称射影联络、半对称共形联络、对称射影共形联络、射影联络、共形联络以及 Levi-Civita联络。在此基础上提出了几种能够满足 Schur定理的半对称射影共形联络的形式,并证明半对称射影共形联络的黎曼流形是常曲率黎曼流形的充分必要条件。
在黎曼流形上定義瞭一箇半對稱射影共形聯絡,併研究瞭其性質,同時指齣這種聯絡在特殊情形下可成半對稱射影聯絡、半對稱共形聯絡、對稱射影共形聯絡、射影聯絡、共形聯絡以及 Levi-Civita聯絡。在此基礎上提齣瞭幾種能夠滿足 Schur定理的半對稱射影共形聯絡的形式,併證明半對稱射影共形聯絡的黎曼流形是常麯率黎曼流形的充分必要條件。
재려만류형상정의료일개반대칭사영공형련락,병연구료기성질,동시지출저충련락재특수정형하가성반대칭사영련락、반대칭공형련락、대칭사영공형련락、사영련락、공형련락이급 Levi-Civita련락。재차기출상제출료궤충능구만족 Schur정리적반대칭사영공형련락적형식,병증명반대칭사영공형련락적려만류형시상곡솔려만류형적충분필요조건。
In Riemannian manifold,we defined a semi-symmetric proj ective conformal connection and consid-ered its properties.In particular cases,this connection reduces to several connections:semi-symmetric proj ec-tive connection,semi-symmetric conformal connection,symmetric proj ective conformal connection,proj ective connection,conformal connection and Levi-Civita connection.We also found forms of a semi-symmetric pro-j ective conformal connection satisfying the Schur’s theorem.And we considered necessary and sufficient condi-tion that a Riemannian manifold with a semi-symmetric proj ective conformal connection be a Riemannian mani-fold with constant curvature.