On Wintgen Ideal Submanifolds Satisfying Some Pseudo-symmetry Type Curvature Conditions

被引：0

作者：

Deszcz, Ryszard ^{[1
]}

Glogowska, Malgorzata ^{[1
]}

Petrovic-Torgasev, Miroslava ^{[2
]}

Zafindratafa, Georges ^{[3
]}

机构：

[1] Wroclaw Univ Environm & Life Sci, Dept Appl Math, Grunwaldzka 53, PL-50357 Wroclaw, Poland

[2] State Univ Novi Pazar, Dept Sci & Math, Vuka Karadz 9, Novi Pazar 36300, Serbia

[3] Univ Polytech Hauts Defrance, Prof Emer Lab Math Ingenieur LMI, F-59313 Valenciennes, France

来源：

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY | 2024年 / 17卷 / 01期

关键词：

Tachibana tensor; pseudo-symmetry type curvature condition; generalized Einstein metric condition; submanifold; Wintgen ideal submanifold; DDVV conjecture; DESZCZ SYMMETRIES; DDVV CONJECTURE; HYPERSURFACES; CLASSIFICATION; THEOREMS;

D O I：

10.36890/IEJG.1404576

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be a Wintgen ideal submanifold of dimension n in a real space form Rn+m ((k) over tilde of dimension (n + m , of constant curvature (k) over tilde, n >= 4, m >= 1. We determine necessary and sufficient conditions for M to be a submanifold satisfying pseudo-symmetry type curvature conditions of the form: the derivation-commutator R.C - C.R (resp., the tensors R.C and C.R formed by the Riemann- Christoffel curvature tensor R and the Weyl conformal curvature tensor C of M, some Tachibana tensors formed by the metric tensor g , the Ricci tensor Ricc and the tensors R and C of M are linearly dependent.

引用

页码：72 / 96

页数：25

共 27 条

[1] On Chen Ideal Submanifolds Satisfying Some Conditions of Pseudo-symmetry Type
Ryszard Deszcz
Miroslava Petrović-Torgas̆ev
Leopold Verstraelen
Georges Zafindratafa
Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39 : 103 - 131
[2] On Chen Ideal Submanifolds Satisfying Some Conditions of Pseudo-symmetry Type
Deszcz, Ryszard
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Verstraelen, Leopold
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BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2016, 39 (01) : 103 - 131
[3] ON THE ROTER TYPE OF WINTGEN IDEAL SUBMANIFOLDS
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[4] PSEUDO-SYMMETRIES OF GENERALIZED WINTGEN IDEAL LAGRANGIAN SUBMANIFOLDS
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PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2018, 103 (117): : 181 - 190
[5] Submanifolds satisfying some curvature conditions imposed on the Weyl tensor
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[6] On the Roter type of generalised Wintgen ideal Legendrian submanifolds
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FILOMAT, 2023, 37 (25) : 8611 - 8616
[7] CHARACTERIZATION OF THE PSEUDO-SYMMETRIES OF IDEAL WINTGEN SUBMANIFOLDS OF DIMENSION 3
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[8] SOME CURVATURE CONDITIONS OF THE TYPE 4 x 2 ON THE SUBMANIFOLDS SATISFYING CHEN'S EQUALITY
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[9] SOME CURVATURE CONDITIONS OF THE TYPE 2 x 4 ON THE SUBMANIFOLDS SATISFYING CHEN'S EQUALITY
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[10] On warped product manifolds satisfying some curvature conditions
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JOURNAL OF GEOMETRY AND PHYSICS, 2013, 74 : 328 - 341

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