NDLI: On the Roter Type of Chen Ideal Submanifolds

Content Provider	Springer Nature Link
Author	Głogowska, Małgorzata Petrović Torgašev, Miroslava Verstraelen, Leopold Deszcz, Ryszard
Copyright Year	2011
Abstract	Chen ideal submanifolds Mnin Euclidean ambient spaces En+m (of arbitrary dimensions n ≥ 2 and codimensions m ≥ 1) at each of their points do realise an optimal equality between their squared mean curvature, which is their main extrinsic scalar valued curvature invariant, and their δ–(= δ(2)–) curvature of Chen, which is one of their main intrinsic scalar valued curvature invariants. From a geometric point of view, the pseudo-symmetric Riemannian manifolds can be seen as the most natural symmetric spaces after the real space forms, i.e. the spaces of constant Riemannian sectional curvature. From an algebraic point of view, the Roter manifolds can be seen as the Riemannian manifolds whose Riemann–Christoffel curvature tensor R has the most simple expression after the real space forms, the latter ones being characterisable as the Riemannian spaces (Mn, g) for which the (0, 4) tensor R is proportional to the Nomizu–Kulkarni square of their (0, 2) metric tensor g. In the present article, for the class of the Chen ideal submanifolds Mn of Euclidean spaces En+m, we study the relationship between these geometric and algebraic generalisations of the real space forms.
Ending Page	413
Page Count	13
Starting Page	401
File Format	PDF
ISSN	14226383
e-ISSN	14209012
Journal	Results in Mathematics
Issue Number	3
Volume Number	59
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2011-04-02
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Chen ideal submanifolds Immersions (minimal, prescribed curvature, tight, etc.) Local Riemannian geometry δ-curvature Roter manifolds Mathematics Local submanifolds Submanifolds pseudo-symmetric manifolds
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Codimension two Kähler submanifolds of space forms

On Submanifolds with 2-Type Pseudo-Hyperbolic Gauss Map in Pseudo-Hyperbolic Space

Ideal CR submanifolds in non-flat complex space forms

N-dimensional totally real minimal submanifolds of CP n

Weakly Convex Biharmonic Hypersurfaces in Nonpositive Curvature Space Forms are Minimal

Splitting Theorems for Submanifolds of Nonnegative Isotropic Curvature

Rigidity Theorems for Manifolds with Boundary and Nonnegative Ricci Curvature

Minimal Submanifolds in Sp+3 with Constant Scalar Curvature

On 2k-Minimal Submanifolds

On the Roter Type of Chen Ideal Submanifolds

Similar Documents

Codimension two Kähler submanifolds of space forms

On Submanifolds with 2-Type Pseudo-Hyperbolic Gauss Map in Pseudo-Hyperbolic Space

Ideal CR submanifolds in non-flat complex space forms

N-dimensional totally real minimal submanifolds of CP n

Weakly Convex Biharmonic Hypersurfaces in Nonpositive Curvature Space Forms are Minimal

Splitting Theorems for Submanifolds of Nonnegative Isotropic Curvature

Rigidity Theorems for Manifolds with Boundary and Nonnegative Ricci Curvature

Minimal Submanifolds in Sp+3 with Constant Scalar Curvature

On 2k-Minimal Submanifolds

On the Roter Type of Chen Ideal Submanifolds