葉聞 宋衛(wèi)東
摘要:建立了單連通完備近擬常曲率空間中具有平行平均曲率向量緊致子流形的廣義J. Simons型積分不等式。將相應(yīng)的結(jié)果推廣到非空間形式中非極小子流形的情形。
關(guān)鍵詞:近擬常曲率空間;平行平均曲率向量;J.Simons型積分不等式
中圖分類號(hào):O 186.16文獻(xiàn)標(biāo)志碼:A文章編號(hào):1001-2443(2023)06-0516-04
由A,B,C,D,E的估計(jì)及Mn的緊性,經(jīng)整理,即完成定理1的證明。
參考文獻(xiàn):
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[2]BAI Z G. Minimal submanifolds in Riemannian manifold of quasi-constant curvature[J].Chin Ann of math,1988,9B(1):32-37.
[3]宋衛(wèi)東,劉敏.關(guān)于擬常曲率空間中具有平行平均曲率向量的子流形[J].安徽師范大學(xué)學(xué)報(bào)(自然科學(xué)版),2007, 29(3):214-219.
[4]王世莉.關(guān)于擬常曲率空間中的偽臍子流形[D].重慶:西南大學(xué),2017:12-26.
[5]耿杰,宋衛(wèi)東.關(guān)于近擬常曲率空間具有常平均曲率超曲面[J].安徽師范大學(xué)學(xué)報(bào)(自然科學(xué)版),2021,44(3):215-218.
[6]葉聞,宋衛(wèi)東,耿杰.關(guān)于近擬常曲率空間中2-調(diào)和子流形[J].安徽師范大學(xué)學(xué)報(bào)(自然科學(xué)版),2022,45(1):13-17.
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On the Submanifolds with Parallel Mean Curvature Vector in Nearly Quasi Constant Curvature Space
YE Wen1, SONG Wei-dong1,2
(1. Faculty of General Education and Foreign Languages, Anhui Institute of Information Technology, Wuhu 241000 , China;
2. School of Mathematics and Statistics, Anhui Normal University , Wuhu 241000, China)
Abstract: In this paper, a generalized J. Simons type integral inequality is established for compact submanifold with parallel mean curvature vectors in a simply connected complete nearly-quasi-constant curvature space. The corresponding results are extended to the case of non-minimal submanifolds in non-spatial forms.
Key words: nearly quasi-constant curvature space; parallel mean curvaturevector; J. Simons type integral inequality
(責(zé)任編輯:馬乃玉)
收稿日期:2023-04-23
基金項(xiàng)目:省級(jí)質(zhì)量工程課程思政項(xiàng)目(2021kcszsfkc200);安徽省高校自然科學(xué)研究項(xiàng)目(2023AH052921).
作者簡介:葉聞(1987—),男,安徽東至縣人,碩士,講師,研究方向:子流形幾何;宋衛(wèi)東(1958—),男,安徽桐城市人,教授,碩士生導(dǎo)師,研究方向:子流形幾何.
引用格式:葉聞,宋衛(wèi)東.近擬常曲率空間中具有平行平均曲率向量的子流形[J].安徽師范大學(xué)學(xué)報(bào)(自然科學(xué)版),2023,46(6):516-519.