共查询到10条相似文献,搜索用时 78 毫秒
1.
Ye-Lin Ou 《Annals of Global Analysis and Geometry》2009,36(2):133-142
This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension
field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface
into Euclidean 3-space. As applications, we construct a two-parameter family of non-minimal conformal biharmonic immersions
of cylinder into and some examples of conformal biharmonic immersions of four-dimensional Euclidean space into sphere and hyperbolic space,
thus providing many simple examples of proper biharmonic maps with rich geometric meanings. These suggest that there are abundant
proper biharmonic maps in the family of conformal immersions. We also explore the relationship between biharmonicity and holomorphicity
of conformal immersions of surfaces.
相似文献
2.
Alfonso Romero 《manuscripta mathematica》1987,59(3):261-276
The rigidity for full holomorphic isometric immersions of an indefinite Kähler manifold into an indefinite complex space form is proved. All such immersions between indefinite complex projective (and hyperbolic) spaces are founded and examples of non-congruents holomorphic isometric immersions are exposed. 相似文献
3.
Like minimal surface immersions in 3-space, pluriharmonic maps into symmetric spaces allow a one-parameter family of isometric deformations rotating the differential (“associated family”); in fact, pluriharmonic maps are characterized by this property. We give a geometric proof of this fact and investigate the “isotropic” case where this family is constant. It turns out that isotropic pluriharmonic maps arise from certain holomorphic maps into flag manifolds. Further, we also consider higher dimensional generalizations of constant mean curvature surfaces which are Kähler submanifolds with parallel (1,1) part of their soecond fundamental form; under certain restrictions there are also characterized by having some kind of (“weak”) associated family. Examples where this family is constant arise from extrinsic Kähler symmetric spaces. 相似文献
4.
Like minimal surface immersions in 3-space, pluriharmonic maps into symmetric spaces allow a one-parameter family of isometric
deformations rotating the differential (“associated family”); in fact, pluriharmonic maps are characterized by this property.
We give a geometric proof of this fact and investigate the “isotropic” case where this family is constant. It turns out that
isotropic pluriharmonic maps arise from certain holomorphic maps into flag manifolds. Further, we also consider higher dimensional
generalizations of constant mean curvature surfaces which are K?hler submanifolds with parallel (1,1) part of their soecond
fundamental form; under certain restrictions there are also characterized by having some kind of (“weak”) associated family.
Examples where this family is constant arise from extrinsic K?hler symmetric spaces.
Received: 8 July 1997 相似文献
5.
Isometric immersions with parallel pluri-mean curvature (“ppmc”) in euclidean n-space generalize constant mean curvature (“cmc”) surfaces to higher dimensional Kähler submanifolds. Like cmc surfaces they allow a one-parameter family of isometric deformations rotating the second fundamental form at each point. If these deformations are trivial the ppmc immersions are called isotropic. Our main result drastically restricts the intrinsic geometry of such a submanifold: Locally, it must be a symmetric space or a Riemannian product unless the immersion is holomorphic or a superminimal surface in a sphere. We can give a precise classification if the codimension is less than 7. The main idea of the proof is to show that the tangent holonomy is restricted and to apply the Berger-Simons holonomy theorem. 相似文献
6.
D. Blanusa 《Annali di Matematica Pura ed Applicata》1962,57(1):321-337
Summary C∞ — isometric imbeddings of the hyperbolic plane and of the two types of orientable cylinders with hyperbolic metric in spherical8-space are constructed, furthermore C∞ — isometric imbeddings of the non-orientable cylinder with hyperbolic metric in Euclidean8-space and in spherical10-space.
To Enrico Bompiani on his scientific Jubilee. 相似文献
7.
Curved flats,pluriharmonic maps and constant curvature immersions into pseudo-Riemannian space forms 总被引:1,自引:0,他引:1
David Brander 《Annals of Global Analysis and Geometry》2007,32(3):253-275
We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first
aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences
between global isometric immersion problems among different space forms and pseudo-Riemannian space forms. As a corollary,
we obtain a non-immersibility theorem for spheres into certain pseudo-Riemannian spheres and hyperbolic spaces. The second
aspect pursued is to clarify the relationship between the loop group formulation of isometric immersions of space forms and
that of pluriharmonic maps into symmetric spaces. We show that the objects in the first class are, in the real analytic case,
extended pluriharmonic maps into certain symmetric spaces which satisfy an extra reality condition along a totally real submanifold.
We show how to construct such pluriharmonic maps for general symmetric spaces from curved flats, using a generalised DPW method.
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8.
The theorem of Beez-Killing in Euclidean differential geometry states as follows [KN, p.46]. Let f: M n → Rn+1 be an isometric immersion of an n-dimensional Riemannian manifold into a Euclidean (n + l)-space. If the rank of the second fundamental form of f is greater than 2 at every point, then any isometric immersion of M n into R n + 1 is congruent to f. A generalization of this classical theorem to affine differential geometry has been given in [O] (see Theorem 1.5). We shall give in this paper another version of rigidity theorem for affine immersions. 相似文献
9.
This paper studies how the behavior of a proper isometric immersion into the hyperbolic space is influenced by its behavior
at infinity. Our first result states that a proper isometric minimal immersion into the hyperbolic space with the asymptotic
boundary contained in a sphere reduces codimension. This result is a corollary of a more general one that establishes a sharp
lower bound for the sup-norm of the mean curvature vector of a Proper isometric immersion into the Hyperbolic space whose
Asymptotic boundary is contained in a sphere. We also prove that a properly immersed hypersurface with mean curvature satisfying sup
p∈Σ ||H(p)|| < 1 has no isolated points in its asymptotic boundary. Our main tool is a Tangency principle for isometric immersions of arbitrary
codimension.
This work is partially supported by CAPES, Brazil. 相似文献
10.
In this article we study isometric immersions from Kähler manifolds whose (1, 1) part of the second fundamental form is parallel, theppmc isometric immersions. When the domain is a Riemann surface these immersions are precisely those with parallel mean curvature. P. J. Ryan has classified the Kähler manifolds that admit isometric immersions, as real hypersurfaces, in space forms. We classify the codimension twoppmc isometric immersions into space forms. 相似文献