Results 231 to 240 of about 7,865 (260)

Submanifolds with totally umbilical Gauss image

Geometriae Dedicata, 1996
The submanifolds whose Gauss images are totally umbilical submanifolds of a Grassmannian manifold are considered. The main result is the following classification theorem: if the Gauss image of a submanifold \(F\) in a Euclidean space is totally umbilical, then either the Gauss image is totally geodesic, or \(F\) is a surface in \(E^n\) of special ...
exaly   +3 more sources

ON TOTALLY UMBILICAL AND SCREEN TOTALLY UMBILICAL RADICAL TRANSVERSAL LIGHTLIKE HYPERSURFACES OF KÄHLER-NORDEN MANIFOLDS

Current Developments in Differential Geometry and its Related Fields, 2015
Galia Nakova
exaly   +2 more sources

Conformal Killing Forms on Totally Umbilical Submanifolds

Journal of Mathematical Sciences, 2016
For a \(C^{\infty}\)-manifold \(M\) with a pseudo-Riemannian metric \(g\) and Levi-Civita connection \(\nabla\), an \(r\)-form \(\omega\) on \(M\) is called a conformal Killing form if it satisfies the differential equation: \[ \nabla\omega-\frac{1}{r+1}d\omega+g\wedge\theta=0 \] for some \((r-1)\)-form \(\theta\).
Stepanov, S. E., Alexandrova, I. A., Tsyganok, I. I., Mikeš, Josef   +3 more
openaire   +2 more sources

On totally umbilical submanifolds ofS n+p

Israel Journal of Mathematics, 2000
Let \(M\) be an \(n\)-dimensional compact minimal submanifold in \(S^{n+p}\). \textit{A. M. Li} and \textit{J. M. Li} proved a scalar curvature pinching theorem [Arch. Math. 58, 582-594 (1992; Zbl 0767.53042)]. \textit{S.-T. Yau} proved a sectional curvature pinching theorem [Am. J. Math. 97, 76-100 (1975; Zbl 0304.53042)]. \textit{N.
openaire   +2 more sources

Totally umbilical CR-submanifolds of Kähler manifolds

TRU Mathematics, 1985
The authors prove the following important result. Any connected non totally geodesic but totally umbilical proper CR-submanifold of dimension greater than 4 in a Kähler manifold is a Sasakian manifold.
TOYONARI, TOSHITAKA, NEMOTO, HIROAKI
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On totally umbilical submanifolds of Finsler spaces

Annales Polonici Mathematici, 2011
The authors define totally umbilical submanifolds of Finsler manifolds using the second fundamental form introduced by Q. He and Y. B. Shen. They study totally umbilical submanifolds of Finsler manifolds establishing some simpler equations related to curvatures of Finsler submanifolds and the curvatures of the ambient space.
He, Qun, Yang, Wei, Zhao, Wei
openaire   +1 more source

Totally umbilical submanifolds inG(2,n). II

Journal of Mathematical Sciences, 1994
A submanifold \(N\) in a Riemannian manifold \(M\) is called totally umbilical if its second fundamental form is proportional to the first fundamental form. In this note, the author continues the study of totally umbilical submanifolds in symmetric spaces. In [the author, Mat. Fiz. Anal. Geom.
openaire   +4 more sources

On a class of submanifolds carrying an extrinsic totally umbilical foliation

Israel Journal of Mathematics, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dajczer, M., Florit, L. A., Tojeiro, R.
openaire   +2 more sources

Rigidity for Closed Totally Umbilical Hypersurfaces in Space Forms

The Journal of Geometric Analysis, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cheng, Xu, Zhou, Detang
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Infusion of Total Parenteral Nutrition via the Umbilical Artery

Journal of Parenteral and Enteral Nutrition, 1991
The administration of total parenteral nutrition through umbilical artery catheters in 48 neonates (birth weight 1.7 ± 0.58 kg) was compared with administration via central venous catheters in 26 infants (birth weight 2.05 ± 0.89 kg). There was no significant difference in the amount of calories delivered (72 ± 12 us 78 ± 18 cal/kg/day) or in the mean ...
K S, Kanarek, M B, Kuznicki, R C, Blair
openaire   +2 more sources