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JournalISSN: 0040-8735

Tohoku Mathematical Journal 

Tohoku University
About: Tohoku Mathematical Journal is an academic journal published by Tohoku University. The journal publishes majorly in the area(s): Scalar curvature & Fourier series. It has an ISSN identifier of 0040-8735. Over the lifetime, 3114 publications have been published receiving 47061 citations. The journal is also known as: Tohoku math. j.


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Journal ArticleDOI
Kazuoki Azuma1
TL;DR: In this paper, a sequence of bounded martingale differences on a probability space is shown to be bounded almost surely (a.s.) for n = 1, 2, etc.
Abstract: 1. Let be a probability space and,be an increasing family of sub o'-fields of(we put(c) Let (xn)n=1, 2, •c be a sequence of bounded martingale differences on , that is,xn(ƒÖ) is bounded almost surely (a.s.) ands. for n =1, 2,.... It is easily seen that this sequence has the following properties[G] and [M], which have been introduced by Y. S. Chow ([1]) in an analogous form and by G. Alexits ([4]), respectively, and may be of independent interest.

1,228 citations

Journal ArticleDOI
TL;DR: In this article, Tanno has classified connected almost contact Riemannian manifolds whose automorphism groups have themaximum dimension into three classes: (1) homogeneous normal contact manifolds with constant 0-holomorphic sec-tional curvature if the sectional curvature for 2-planes which contain
Abstract: Recently S. Tanno has classified connected almostcontact Riemannian manifolds whose automorphism groups have themaximum dimension [9]. In his classification table the almost contactRiemannian manifolds are divided into three classes: (1) homogeneousnormal contact Riemannian manifolds with constant 0-holomorphic sec-tional curvature if the sectional curvature for 2-planes which contain

614 citations

Journal ArticleDOI
Shigeo Sasaki1
TL;DR: In this paper, a Riemannian metric on the tangent sphere-bundles of the manifold T{M] was introduced, and the geodesic flow on it was considered.
Abstract: H.Poincare used the tangent sphere-bundles of ovaloids in three dimensional Euclidean space, i.e. the phase spaces of the ovaloids, to prove the existence of certain closed geodesies on the ovaloids. He introduced a Riemannian metric on the tangent sphere-bundles and considered the geodesic flow on it. As the metric of tangent bundles of Riemannian manifolds seems to be important, we would like to study differential geometry of tangent bundles of Riemannian manifolds by introducing on it natural Riemannian metrics. In this papar we shall do it by restricting ourselves only to the tangent bundles T{M).

523 citations

Performance
Metrics
No. of papers from the Journal in previous years
YearPapers
202316
202229
20217
202023
201923
201822