共查询到20条相似文献,搜索用时 15 毫秒
1.
Gerard Walschap 《Journal of Geometric Analysis》1992,2(4):373-381
We prove a rigidity theorem for Riemannian fibrations of flat spaces over compact bases and give a metric classification of compact four-dimensional manifolds of nonnegative curvature that admit totally geodesic Riemannian foliations. 相似文献
2.
1980Mathematics Subject Classification (1985Revision): 53C12, 57R30 相似文献
3.
Gen-Ichi Oshikiri 《Commentarii Mathematici Helvetici》1990,65(1):79-84
The author is partially supported by a grant from the Alexander von Humboldt Foundation. 相似文献
4.
A. A. Borisenko 《Mathematical Notes》1997,62(5):562-565
The topological structure of compact Riemannian manifolds that admit hyperbolic foliations is studied.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 673–676, November, 1997.
Translated by S. S. Anisov 相似文献
5.
WANG PeiHe & WEN YuLiang School of Mathematical Sciences Qufu Normal University Qufu China 《中国科学 数学(英文版)》2011,(3)
Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2 4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n. 相似文献
6.
Gen-ichi Oshikiri 《Mathematische Zeitschrift》1990,203(1):105-113
The author is partially supported by a grant from the Alexander von Humboldt Foundation 相似文献
7.
Gromoll and Meyer have represented a certain exotic 7-sphere as a biquotient of the Lie group . We show for a 2-parameter family of left invariant metrics on that the induced metric on has strictly positive sectional curvature at all points outside four subvarieties of codimension which we describe explicitly.
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10.
Gen-ichi Oshikiri 《Commentarii Mathematici Helvetici》1991,66(1):512-520
Dedicated to Professor Haruo Suzuki on his sixtieth birthday 相似文献
11.
The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4‐manifolds. In addition, we provide topological sphere theorems for compact submanifolds of spheres and Euclidean spaces, provided that the full norm of the second fundamental form is suitably bounded. 相似文献
12.
Jesús A. Alvarez López 《Annals of Global Analysis and Geometry》1992,10(2):179-194
For a Riemannian foliation % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\] on a compact manifold M with a bundle-like metric, the de Rham complex of M is C-splitted as the direct sum of the basic complex and its orthogonal complement. Then the basic component % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacciGae8NUdS% 2aaSbaaSqaaiaadkgaaeqaaaaa!38B9!\[\kappa _b \] of the mean curvature form of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\] is closed and defines a class (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\]) in the basic cohomology that is invariant under any change of the bundle-like metric. Moreover, any element in (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\]) can be realized as the basic component of the mean curvature of some bundle-like metric.It is also proved that (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\]) vanishes iff there exists some bundle-like metric on M for which the leaves are minimal submanifolds. As a consequence, this tautness property is verified in any of the following cases: (a) when the Ricci curvature of the transverse Riemannian structure is positive, or (b) when % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\] is of codimension one. In particular, a compact manifold with a Riemannian foliation of codimension one has infinite fundamental group. 相似文献
13.
D. Gabai 《Commentarii Mathematici Helvetici》2000,75(1):109-124
A -injective closed surface in an orientable 3-manifold with a tangentially smooth, transversely C 0 taut foliation can be homotoped to an immersed surface which is either transverse to the foliation except at isolated saddle tangencies or mapped into a leaf. Received: November 11, 1997 相似文献
14.
Yu. S. Ilyashenko 《Proceedings of the Steklov Institute of Mathematics》2007,259(1):60-72
Polynomial foliations of the complex plane are topologically rigid. Roughly speaking, this means that the topological equivalence
of two foliations implies their affine equivalence. There exist various nonequivalent formalizations of the notion of topological
rigidity. Generic polynomial foliations of fixed degree have the so-called property of absolute rigidity, which is the weakest
form of topological rigidity. This property was discovered by the author more than 30 years ago. The genericity conditions
imposed at that time were very restrictive. Since then, this topic has been studied by Shcherbakov, Gómez-Mont, Nakai, Lins
Neto-Sad-Scárdua, Loray-Rebelo, and others. They relaxed the genericity conditions and increased the dimension. The main conjecture
in this field states that a generic polynomial foliation of the complex plane is topologically equivalent to only finitely
many foliations. The main result of this paper is weaker than this conjecture but also makes it possible to compare topological
types of distant foliations. 相似文献
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16.
Yu. S. Ilyashenko 《Proceedings of the Steklov Institute of Mathematics》2007,259(2):60-72
Polynomial foliations of the complex plane are topologically rigid. Roughly speaking, this means that the topological equivalence
of two foliations implies their affine equivalence. There exist various nonequivalent formalizations of the notion of topological
rigidity. Generic polynomial foliations of fixed degree have the so-called property of absolute rigidity, which is the weakest
form of topological rigidity. This property was discovered by the author more than 30 years ago. The genericity conditions
imposed at that time were very restrictive. Since then, this topic has been studied by Shcherbakov, Gómez-Mont, Nakai, Lins
Neto-Sad-Scárdua, Loray-Rebelo, and others. They relaxed the genericity conditions and increased the dimension. The main conjecture
in this field states that a generic polynomial foliation of the complex plane is topologically equivalent to only finitely
many foliations. The main result of this paper is weaker than this conjecture but also makes it possible to compare topological
types of distant foliations.
Original Russian Text ? Yu. S. Ilyashenko, 2007, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007,
Vol. 259, pp. 64–76.
To Vladimir Igorevich Arnold with admiration and love 相似文献
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18.
A. Eremenko 《Proceedings of the American Mathematical Society》2004,132(11):3349-3355
A simple proof is given of the necessary and sufficient condition on a triple of positive numbers for the existence of a conformal metric of constant positive curvature on the sphere, with three conic singularities of total angles . The same condition is necessary and sufficient for the triple to be interior angles of a spherical triangular membrane.
19.
Dzan Jin Jee 《Journal of Geometry》1985,24(1):6-13
In this work we set up trigonometric laws and a new parallel angle formula on S
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in terms of Lorentz lengths and pseudo-angles. Thus all the laws have the same form as those of spherical trigonometry. The new parallel angle formula, however, contrasts well with that of Lobatschevsky in hyperbolic geometry. 相似文献
20.
A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern–Moser tensor in CR geometry. It is shown that a quaternionic contact manifold is locally quaternionic contact conformal to the standard flat quaternionic contact structure on the quaternionic Heisenberg group, or equivalently, to the standard 3-Sasakian structure on the sphere iff the quaternionic contact conformal curvature vanishes. 相似文献