共查询到20条相似文献,搜索用时 15 毫秒
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Joel L. Weiner 《Mathematische Annalen》1984,269(4):541-560
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We show that locally conformally flat gradient Ricci solitons, possibly incomplete, are locally isometric to a warped product of an interval and a space form. Consequently, we get that complete gradient shrinking and steady Ricci solitons with vanishing Weyl tensor are rotationally symmetric, from which their classification follows. 相似文献
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Oscar J. Garay 《Annals of Global Analysis and Geometry》1994,12(1):79-86
We classify orthogonal surfaces ofE
4 whose mean curvature is constant by proving that they are either of 1-type or of 2-type.Partially supported by a ME/Fulbright grant and by a DGICYT grant PB91-0705-C02-01 相似文献
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It is proved that, in Minkowski 3-space, a CSM-helicoidal surface, i.e., a helicoidal surface under cubic screw motion is isometric to a rotation surface so that helices on the helicoidal surface correspond to parallel circles on the rotation surface. By distinguishing a CSM-helicoidal surface as three cases, that is, the case of type I, the case of type II with negative and positive pitch, the relations are discussed between the mean curvatures or Gauss maps of a pair of isometric helicoidal and rotation surface. A CSM-helicoidal surface of Case 1 or 2 and its isometric rotation surface with null axis have same mean curvatures (resp. Gauss maps) if and only if they are minimal. But each pair of isometric CSM-helicoidal surface of Case 3 and rotation surface with spacelike axis have different Gauss maps. 相似文献
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Dae Won Yoon 《Central European Journal of Mathematics》2010,8(3):430-436
In this paper, we classify polynomial translation surfaces in Euclidean 3-space satisfying the Jacobi condition with respect
to the Gaussian curvature, the mean curvature and the second Gaussian curvature. 相似文献
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Luc Vrancken 《Monatshefte für Mathematik》1996,122(3):251-264
Surfaces which are both affine and Euclidean minimal are called Thomsen surfaces. In 3, these surfaces have been completely classified byBarthel, Volkmer andHaubitz. A similar problem, in the Lorentzian 3-space was solved byMagid. In the present paper, we study Thomsen surfaces in 4 and show that these surfaces are affine equivalent to the complex paraboloid.The author is a Senior Research Assistant of the National Fund, for Scientific Research (Belgium). This work was done while the author visited Brown University (Providence, USA) in April 93. He would like to thank Professors T. Cecil, M. Magid, and K. Nomizu for their hospitality. 相似文献
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Toru Sasahara 《Archiv der Mathematik》2012,99(3):281-287
A submanifold is said to be tangentially biharmonic if the bitension field of the isometric immersion that defines the submanifold has vanishing tangential component. The purpose of this paper is to prove that a surface in Euclidean 3-space has tangentially biharmonic normal bundle if and only if it is either minimal, a part of a round sphere, or a part of a circular cylinder. 相似文献
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Ronaldo Alves Garcia Dirce Kiyomi Hayashida Mochida Maria del Carmen Romero Fuster Maria Aparecida Soares Ruas 《Transactions of the American Mathematical Society》2000,352(7):3029-3043
We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincaré-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.
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Donghe Pei Lingling Kong Jianguo Sun Qi Wang 《Journal of Mathematical Analysis and Applications》2012,385(1):243-253
The main goal of this paper is to study singularities of lightlike torus Gauss maps of Lorentzian surfaces (i.e., both tangent plane and normal plane are Lorentz) in semi-Euclidean 4-space with index 2. To do this, we construct a Lorentzian lightlike torus height function and reveal relations between singularities of the Lorentzian lightlike torus height function and those of lightlike torus Gauss map. In addition we study some properties of Lorentzian surface from geometrical viewpoint. 相似文献
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On any timelike surface with zero mean curvature in the four-dimensional Minkowski space we introduce special geometric (canonical) parameters and prove that the Gauss curvature and the normal curvature of the surface satisfy a system of two natural partial differential equations. Conversely, any two solutions to this system determine a unique (up to a motion) timelike surface with zero mean curvature so that the given parameters are canonical. We find all timelike surfaces with zero mean curvature in the class of rotational surfaces of Moore type. These examples give rise to a one-parameter family of solutions to the system of natural partial differential equations describing timelike surfaces with zero mean curvature. 相似文献
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Shyuichi Izumiya Donghe Pei María del Carmen Romero Fuster 《Israel Journal of Mathematics》2006,154(1):361-379
We study some geometrical properties associated to the contacts of surfaces with hyperhorospheres inH
+
4
(−1). We introduce the concepts of osculating hyperhorospheres, horobinormals, horoasymptotic directions and horospherical
points and provide conditions ensuring their existence. We show that totally semiumbilical surfaces have orthogonal horoasymptotic
directions.
Work partially supported by Grant-in-Aid for Scientific Research, JSPS, No. 12874007.
Work partially supported by Grant-in-Aid for Scientific Research, JSPS, No. 12000266.
Work partially supported by DGCYT grant no. BFM2003-02037. 相似文献
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Stefan Haesen 《Journal of Mathematical Analysis and Applications》2009,355(2):639-648
A spacelike surface in a Lorentzian manifold whose mean curvature vector is lightlike everywhere is called marginally trapped. The classification of marginally trapped surfaces in Minkowski 4-space which are invariant under a subgroup of the Lorentz group that leaves invariant a lightlike direction, i.e. the so-called screw invariant surfaces, is obtained. As corollaries, the screw invariant marginally trapped surfaces with harmonic mean curvature vector and with prescribed Gaussian curvature are explicitly described. 相似文献
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We show that a compact Riemannian manifold with weakly pointwise 1/4-pinched sectional curvatures is either locally symmetric
or diffeomorphic to a space form. More generally, we classify all compact, locally irreducible Riemannian manifolds M with the property that M × R
2 has non-negative isotropic curvature.
The first author was partially supported by a Sloan Foundation Fellowship and by NSF grant DMS-0605223. The second author
was partially supported by NSF grant DMS-0604960. 相似文献
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We study the singularities of de Sitter Gauss map of timelike hypersurface in Minkowski 4-space through their contact with hyperplanes. 相似文献
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Bang-yen Chen 《Journal of Geometry》1983,20(1):122-127
A surface in Em is said to have planar normal sections if normal sections of M are planar curves. In this paper we completely classify surfaces in Em with planar normal sections. Consequently, a new characterization of the Veronese surface is obtained. 相似文献
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本文考虑欧氏空间中具有共形Gauss映照的曲面.从Gauss映照的观点给出了 veronese曲面的一个新特征. 相似文献