[图书][B] Pseudo-Riemannian geometry,[delta]-invariants and applications
BY Chen - 2011 - books.google.com
The first part of this book provides a self-contained and accessible introduction to the subject
in the general setting of pseudo-Riemannian manifolds and their non-degenerate …
in the general setting of pseudo-Riemannian manifolds and their non-degenerate …
[图书][B] Total mean curvature and submanifolds of finite type
BY Chen - 2014 - books.google.com
During the last four decades, there were numerous important developments on total mean
curvature and the theory of finite type submanifolds. This unique and expanded second …
curvature and the theory of finite type submanifolds. This unique and expanded second …
A short survey on biharmonic maps between Riemannian manifolds
S Montaldo, C Oniciuc - Revista de la Unión Matemática …, 2006 - SciELO Argentina
A short survey on biharmonic maps between Riemannian manifolds SciELO - Scientific
Electronic Library Online vol.47 número2 II Encuentro de Geometría Diferencial: 6 al 11 de junio …
Electronic Library Online vol.47 número2 II Encuentro de Geometría Diferencial: 6 al 11 de junio …
[PDF][PDF] Biharmonic submanifolds of Kähler product manifolds
In this paper, the authors have established the necessary and sufficient conditions for the
submanifolds of Kaehler product manifolds to be biharmonic. Moreover, the magnitude of …
submanifolds of Kaehler product manifolds to be biharmonic. Moreover, the magnitude of …
Recent developments of biharmonic conjecture and modified biharmonic conjectures
BY Chen - arXiv preprint arXiv:1307.0245, 2013 - arxiv.org
A submanifold $ M $ of a Euclidean $ m $-space is said to be biharmonic if
$\Delta\overrightarrow H= 0$ holds identically, where $\overrightarrow H $ is the mean …
$\Delta\overrightarrow H= 0$ holds identically, where $\overrightarrow H $ is the mean …
Biharmonic maps into a Riemannian manifold of non-positive curvature
N Nakauchi, H Urakawa, S Gudmundsson - Geometriae Dedicata, 2014 - Springer
We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-
energy. We show that if the domain is complete and the target of non-positive curvature, then …
energy. We show that if the domain is complete and the target of non-positive curvature, then …
Explicit formulas for non-geodesic biharmonic curves of the Heisenberg group
R Caddeo, C Oniciuc, P Piu - arXiv preprint math/0311221, 2003 - arxiv.org
arXiv:math/0311221v1 [math.DG] 13 Nov 2003 Page 1 arXiv:math/0311221v1 [math.DG] 13
Nov 2003 EXPLICIT FORMULAS FOR NON-GEODESIC BIHARMONIC CURVES OF THE …
Nov 2003 EXPLICIT FORMULAS FOR NON-GEODESIC BIHARMONIC CURVES OF THE …
Some open problems and conjectures on submanifolds of finite type: recent development
BY Chen - arXiv preprint arXiv:1401.3793, 2014 - arxiv.org
Submanifolds of finite type were introduced by the author during the late 1970s. The first
results on this subject were collected in author's books [26, 29]. In 1991, a list of twelve open …
results on this subject were collected in author's books [26, 29]. In 1991, a list of twelve open …
Biharmonic submanifolds in a Riemannian manifold with non-positive curvature
N Nakauchi, H Urakawa - Results in mathematics, 2013 - Springer
In this paper, we show that, for every biharmonic submanifold (M, g) of a Riemannian
manifold (N, h) with non-positive sectional curvature, if\int_M | η |^ 2 v_g< ∞, then (M, g) is …
manifold (N, h) with non-positive sectional curvature, if\int_M | η |^ 2 v_g< ∞, then (M, g) is …
Biharmonic hypersurfaces in a Riemannian manifold with non-positive Ricci curvature
N Nakauchi, H Urakawa - Annals of global analysis and geometry, 2011 - Springer
In this article, we show that, for a biharmonic hypersurface (M, g) of a Riemannian manifold
(N, h) of non-positive Ricci curvature, if\int_M | H |^ 2 v_g< ∞, where H is the mean curvature …
(N, h) of non-positive Ricci curvature, if\int_M | H |^ 2 v_g< ∞, where H is the mean curvature …