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11.
Yu Fu 《Mathematische Nachrichten》2015,288(7):763-774
We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmu?‐Montaldo‐Oniciuc, we prove that compact orientable proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces are either the hypersphere or the Clifford hypersurface with and . Moreover, we also show that there does not exist proper biharmonic hypersurface with at most three distinct principal curvatures in hyperbolic spaces . 相似文献
12.
We give a new proof of the generalized Minkowski identities relating the higher degree mean curvatures of orientable closed hypersurfaces immersed in a given constant sectional curvature manifold. Our methods rely on a fundamental differential system of Riemannian geometry introduced by the author. We develop the notion of position vector field, which lies at the core of the Minkowski identities. 相似文献
13.
Erwann Delay 《Advances in Mathematics》2002,168(2):213-224
On an asymptotically hyperbolic Einstein manifold (M,g0) for which the Yamabe invariant of the conformal structure on the boundary at infinity is nonnegative, we show that the operators of Ricci curvature, and of Einstein curvature, are locally invertible in a neighborhood of the metric g0. We deduce in the C∞ case that the image of the Riemann-Christoffel curvature operator is a submanifold in a neighborhood of g0. 相似文献
14.
The hypothesis of coupling between spin and rotation introduced long ago by Mashhoon is examined in the context of “1 + 3”
and “3 + 1” space-time splitting techniques, either in special or in general relativity. Its content is discussed in terms
of classical (Mathisson–Papapetrou–Dixon–Souriou model) as well as quantum physics (Foldy–Wouthuysen transformation for the
Dirac field in an external field), reviewing and discussing all the relevant theoretical literature concerning the existence
of such effect. Some original contributions are also included.
Dedicated to Bahram Mashhoon for his 60th birthday. 相似文献
15.
Fábio Dahia Carlos Romero Lúcio F. P. da Silva Reza Tavakol 《General Relativity and Gravitation》2008,40(6):1341-1351
We study the classical geodesic motions of nonzero rest mass test particles and photons in (3 + 1 + n)- dimensional warped product spaces. An important feature of these spaces is that they allow a natural decoupling between
the motions in the (3 + 1)-dimensional spacetime and those in the extra n dimensions. Using this decoupling and employing phase space analysis we investigate the conditions for confinement of particles
and photons to the (3 + 1)- spacetime submanifold. In addition to providing information regarding the motion of photons, we
also show that these motions are not constrained by the value of the extrinsic curvature. We obtain the general conditions
for the confinement of geodesics in the case of pseudo-Riemannian manifolds as well as establishing the conditions for the
stability of such confinement. These results also generalise a recent result of the authors concerning the embeddings of hypersurfaces
with codimension one. 相似文献
16.
Wenxiong Chen & Ruobing Zhang 《数学研究》2020,53(4):436-470
In this paper, we will explore the geometric effects of conformally covariant
operators and the induced nonlinear curvature equations in certain nonlocal nature.
Mainly, we will prove some regularity and rigidity results for the distributional solutions to those equations. 相似文献
17.
We prove anisotropic Reilly-type upper bounds for divergence-type operators on hypersurfaces of the Euclidean space in presence of a weighted measure. 相似文献
18.
The Kähler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kähler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kähler metrics into Kähler ones is introduced and biconformal tensor invariants are obtained. This makes it possible to classify the manifolds under consideration locally. The class of locally biconformal flat Kähler metrics is shown to be exactly the class of Kähler metrics whose potential function is only a function of the distance from the origin in ? n . Finally we show that any rotational even dimensional hypersurface carries locally a natural Kähler structure which is of quasi-constant holomorphic sectional curvatures. 相似文献
19.
Monika Ludwig 《Mathematische Nachrichten》2001,227(1):99-108
Let Hj(K, ·) be the j – th elementary symmetric function of the principal curvatures of a convex body K in Euclidean d – space. We show that the functionals ∫bd f(Hj(K, x)) dℋ︁d—1(x) depend upper semicontinuously on K, if f : [0, ∞) is concave, limt→0f(t) = 0, and limt→∞f(t)/t = 0. An analogous statement holds for integrals of elementary symmetric functions of the principal radii of curvature. 相似文献
20.
We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide
a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the
homogeneous hypersurfaces together with their multiplicities.
相似文献