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1.
2.
SHARIEF DESHMUKH 《Proceedings Mathematical Sciences》2011,121(2):171-179
In this paper, we classify real hypersurfaces in the complex projective space
C P\fracn+12C P^{\frac{n+1}{2}} whose structure vector field is a φ-analytic vector field (a notion similar to analytic vector fields on complex manifolds). We also define Jacobi-type vector
fields on a Riemannian manifold and classify real hypersurfaces whose structure vector field is a Jacobi-type vector field. 相似文献
3.
We characterize homogeneous real hypersurfaces M's of type (A
1), (A
2) and (B) of a complex projective space in the class of real hypersurfaces by studying the holomorphic distribution T
0
M of M. 相似文献
4.
Qing-Ming Cheng 《manuscripta mathematica》1994,82(1):149-160
In this paper, we prove that the hyperbolic cylinderH
1(c
1)×H
2(c
2) is the only complete maximal spacelike hypersurfaces inH
1
4
(c) with nonzero constant Gauss-Kronecker curvature and give a characterization of complete maximal spacelike hypersurfaces
ofH
1
4
(c) with constant scalar curvature.
The project Supported by NNSFC, FECC and CPF 相似文献
5.
In this article we study sets in the (2n + 1)-dimensional Heisenberg group ℍ
n
which are critical points, under a volume constraint, of the sub-Riemannian perimeter associated to the distribution of horizontal
vector fields in ℍ
n
.We define a notion of mean curvature for hypersurfaces and we show that the boundary of a stationary set is a constant mean
curvature (CMC) hypersurface. Our definition coincides with previous ones.
Our main result describes which are the CMC hypersurfaces of revolution in ℍ
n
.The fact that such a hypersurface is invariant under a compact group of rotations allows us to reduce the CMC partial differential
equation to a system of ordinary differential equations. The analysis of the solutions leads us to establish a counterpart
in the Heisenberg group of the Delaunay classification of constant mean curvature hypersurfaces of revolution in the Euclidean
space. Hence, we classify the rotationally invariant isoperimetric sets in ℍ
n
. 相似文献
6.
We establish a C2 a priori estimate for convex hypersurfaces whose principal curvatures κ=(κ1,…, κn) satisfy σk(κ(X))=f(X,ν(X)), the Weingarten curvature equation. We also obtain such an estimate for admissible 2‐convex hypersurfaces in the case k=2. Our estimates resolve a longstanding problem in geometric fully nonlinear elliptic equations.© 2015 Wiley Periodicals, Inc. 相似文献
7.
The purpose of this paper is to make clear the so-called Nomizu problem, whether it is possible to find examples of space-like
isoparametric hypersurfaces in H
1
n+1 with more than two distinct principal curvatures. It is proved that a space-like isoparametric hypersurface in H
1
n+1 or S
1
n+1 can have at most two distinct principal curvatures. The authors present the classification and explicit analytic expressions
of such type of isoparametric hypersurfaces.
This paper was translated from J. Nanchang Univ. Nat. Sci. Ed., 2004, 28(2): 113–117 相似文献
8.
In this paper, we study closed k-maximal spacelike hypersurfaces M
n
in anti-de Sitter space H
1
n+1 (−1) with two distinct principal curvatures and give some integral formulas about these hypersurfaces.
The first author was supported by Japan Society for Promotion of Science. The third author was supported by grant Proj. No.
R17-2008-001-01000-0 from Korea Science & Engineering Foundation. 相似文献
9.
Mayuko Kon 《Czechoslovak Mathematical Journal》2008,58(4):1279-1287
We give a characterization of totally η-umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition
for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator A of a real hypersurface M of a complex space form M
n
(c), c ≠ 0, n ⩾ 3, satisfies g(AX, Y) = ag(X, Y) for any X, Y ∈ T
0(x), a being a function, where T
0 is the holomorphic distribution on M, then M is a totally η-umbilical real hypersurface or locally congruent to a ruled real hypersurface. This condition for the shape operator is a
generalization of the notion of η-umbilical real hypersurfaces. 相似文献
10.
A hypersurface f : M → Rn+1 in an affine (n+1)-space is called centroaffine if its position vector is always transversal to f*(TM) in Rn+1. In this paper, we establish a general optimal inequality for definite centroaffine hypersurfaces in Rn+1 involving the Tchebychev vector field. We also completely classify the hypersurfaces which verify the equality case of the inequality. 相似文献
11.
The complex two-plane Grassmannian carries a K?hler structure J and also a quaternionic K?hler structure ?. For we consider the classes of connected real hypersurfaces (M, g) with normal bundle such that and are invariant under the action of the shape operator. We prove that the corresponding unit Hopf vector fields on these hypersurfaces always define minimal immersions of (M, g), and harmonic maps from (M, g), into the unit tangent sphere bundle with Sasaki metric . The radial unit vector fields corresponding to the tubular hypersurfaces are also minimal and harmonic. Similar results hold for the dual space . 相似文献
12.
Given a positive function F on S^n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in R^n+1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in R^n+1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F=1 which reduces to some well-known results. 相似文献
13.
Jean-Pierre Ezin Marco Rigoli Isabel M. C. Salavessa 《Israel Journal of Mathematics》1990,71(2):193-209
We extend some rigidity results of Aleksandrov and Ros on compact hypersurfaces inR
n
to more general ambient spaces with the aid of the notion of almost conformal vector fields. These latter, at least locally,
always exist and allow us to find interesting integral formulas fitting our purposes. 相似文献
14.
Krzysztof Andrzejewski Pawe? G. Walczak 《Differential Geometry and its Applications》2011,29(6):723-729
In this paper, we study hypersurfaces with constant rth mean curvature Sr. We investigate the stability of such hypersurfaces in the case when they are leaves of a codimension one foliation. We also generalize recent results by Barros and Sousa, concerning conformal fields, to an arbitrary manifold. Using this we show that normal component of a Killing field is an rth Jacobi field of a hypersurface with Sr+1 constant. Finally, we study relations between rth Jacobi fields and vector fields preserving a foliation. 相似文献
15.
The complex two-plane Grassmannian carries a K?hler structure J and also a quaternionic K?hler structure ?. For we consider the classes of connected real hypersurfaces (M, g) with normal bundle such that and are invariant under the action of the shape operator. We prove that the corresponding unit Hopf vector fields on these hypersurfaces
always define minimal immersions of (M, g), and harmonic maps from (M, g), into the unit tangent sphere bundle with Sasaki metric . The radial unit vector fields corresponding to the tubular hypersurfaces are also minimal and harmonic. Similar results
hold for the dual space .
(Received 27 August 1999; in revised form 18 November 1999) 相似文献
16.
Jawher El Goul 《manuscripta mathematica》1996,90(1):521-532
We reprove (after a paper of Y.T. Siu appeared in 1987) a simple vanishing theorem for the Wronskian of Brody curves under
a suitable assumption on the existence of global meromorphic connections. Next we give a slight improvement of a result due
to Y.T, Siu and A.M. Nadel (Duke Math. J., 1989) on the algebraic degeneracy of entire holomorphic curves contained in certain
hypersurfaces of ℙ
ℂ
n
. Especially, their result is generalized to a larger class of hypersurfaces. Our method produces algebraic families of smooth
hyperbolic surfaces in ℙ
ℂ
3
for all degreesd≥14; this brings us somewhat nearer than previously known from the expected ranged≥5. 相似文献
17.
Georges Zafindratafa 《Journal of Geometry》1996,55(1-2):182-191
We define finite mean type hypersurfaces to be hypersurfaces with mean curvature function of finite Chen-type. Then, we prove that hyperplanes are the only polynomial translation hypersurfaces of finite mean type in a Euclidean spaceE
n+1. And we show that the only non-conic hyperquadrics of finite mean type in Euclidean spaces are the hyperspheres and the cylinders on spheres. Finally, we state that, among all hypercylinders in a Euclidean spaceE
n+1, the only ones of finite mean type are those on finite mean type planar curves. 相似文献
18.
The sphere S
n+1 contains a simple family of constant mean curvature (CMC) hypersurfaces of the form C
t
: = S
p
(cos t) × S
q
(sin t) for p + q = n and called the generalized Clifford hypersurfaces. This paper demonstrates that new, topologically non-trivial CMC hypersurfaces
resembling a pair of neighbouring generalized Clifford tori connected to each other by small catenoidal bridges at a sufficiently
symmetric configuration of points can be constructed by perturbative PDE methods. That is, one can create an approximate solution
by gluing a rescaled catenoid into the neighbourhood of each point; and then one can show that a perturbation of this approximate
hypersurface exists, which satisfies the CMC condition. The results of this paper generalize those of the authors in [3]. 相似文献
19.
Silvano Delladio 《Journal of Geometric Analysis》2001,11(1):17-42
We show that the L
p
norm of the second fundamental form of hypersurfaces in
R
n+1
is very coercive in the GMT setting of Gauss graphs currents, when p exceeds the dimension n. A compactness result for immersed
hypersurfaces and its application to a variational problem are provided. 相似文献
20.
The purpose of this paper is to give a characterization of real hypersurfaces of type A0, A in a quaternionic hyperbolic space
QH
m by the covariant derivative of the second fundamental tensor.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献