Weakly Einstein Equivalence in a Golden Space Form and Certain CR-submanifolds

被引：1

作者：

Kim, Jihun ^{[1
]}

Park, Jeonghyeong ^{[1
]}

Sahin, Bayram ^{[2
]}

机构：

[1] Sungkyunkwan Univ, Dept Math, 2066 Seobu Ro, Suwon 16419, South Korea

[2] Ege Univ, Fac Sci, Dept Math, TR-35100 Izmir, Turkiye

来源：

MATHEMATICA SLOVACA | 2023年 / 73卷 / 06期

基金：

新加坡国家研究基金会;

关键词：

Golden structure; Golden Riemannian manifold; CR-submanifold; space form; Einstein manifold;

D O I：

10.1515/ms-2023-0117

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that the Golden space form may not be an Einstein manifold. In this paper, it is shown that the condition to be Einstein for a Golden space form is equivalent to being weakly Einstein. In addition, the partial geodesic and cyclic parallelism of the CR-submanifolds of a Golden space are examined, and the case of the constant Golden sectional curvature is determined. Moreover, the CR-submanifolds with semi-flat normal connection are studied and an inequality is obtained. The equality case of this inequality is also checked. We also consider the totally umbilical CR-submanifold of Golden Riemannian manifolds and show that such submanifolds are totally geodesic under certain conditions. Furthermore, we obtain an inequality involving the scalar curvature of CR-submanifold and check the existence of extrinsic spheres in Golden space forms.

引用

页码：1615 / 1627

页数：13

共 48 条

[21] CERTAIN CONDITION ON THE SECOND FUNDAMENTAL FORM OF CR SUBMANIFOLDS OF MAXIMAL CR DIMENSION OF COMPLEX PROJECTIVE SPACE
Djoric, Mirjana
Okumura, Masafumi
ISRAEL JOURNAL OF MATHEMATICS, 2009, 169 (01) : 47 - 59
[22] Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex hyperbolic space
Mirjana Djorić
Masafumi Okumura
Annals of Global Analysis and Geometry, 2011, 39 : 1 - 12
[23] Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex Euclidean space
Mirjana Djorić
Masafumi Okumura
Annals of Global Analysis and Geometry, 2006, 30 : 383 - 396
[24] Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex hyperbolic space
Djoric, Mirjana
Okumura, Masafumi
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2011, 39 (01) : 1 - 12
[25] Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex Euclidean space
Djoric, Mirjana
Okumura, Masafumi
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2006, 30 (04) : 383 - 396
[26] Commutative condition on the second fundamental form of CR-submanifolds of maximal CR-dimension of a Kuhler manifold
Djoric, M
COMPLEX, CONTACT AND SYMMETRIC MANIFOLDS: IN HONOR OF L. VANHECKE, 2005, 234 : 105 - 120
[27] SOME REMARKS ON CR-SUBMANIFOLDS OF A LOCALLY CONFORMAL KAEHLER MANIFOLD WITH PARALLEL LEE FORM
PAPAGHIUC, N
PUBLICATIONES MATHEMATICAE-DEBRECEN, 1993, 43 (3-4): : 337 - 341
[28] Certain CR submanifolds of maximal CR dimension of complex space forms
Djoric, Mirjana
Okumura, Masafumi
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2008, 26 (02) : 208 - 217
[29] RICCI RECURRENT CR SUBMANIFOLDS OF A COMPLEX SPACE FORM
Kon, Mayuko
TSUKUBA JOURNAL OF MATHEMATICS, 2007, 31 (02) : 233 - 252
[30] CR-submanifolds of Chen-type two in non-flat complex space forms
Dimitric, Ivko
Djoric, Mirjana
GEOMETRY OF SUBMANIFOLDS, 2020, 756 : 97 - 110

← 1 2 3 4 5 →