Search Results 1-20 of 422

  • Approximated logarithmic maps on Riemannian manifolds and their applications

    Goto Jumpei , Sato Hiroyuki

    … Recently, optimization problems on Riemannian manifolds involving geodesic distances have been attracting considerable research interest. … To compute geodesic distances and their Riemannian gradients, we can use logarithmic maps. … However, the computational cost of logarithmic maps on Riemannian manifolds is generally higher than that on the Euclidean space. …

    JSIAM Letters 13(0), 17-20, 2021

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  • Spectral analysis on pseudo-Riemannian locally symmetric spaces

    KASSEL Fanny , KOBAYASHI Toshiyuki

    Proceedings of the Japan Academy. Series. A, Mathematical sciences 96(8), 69-74, 2020-10

  • LEAFWISE COHOMOLOGICAL EXPRESSION OF DYNAMICAL ZETA FUNCTIONS ON FOLIATED DYNAMICAL SYSTEMS

    Kim Junhyeong

    … A Riemmanian foliated dynamical system of 3-dimension (RFDS3)is a closed Riemannian 3-manifold with additional structures: foliation, dynamical system. … In this paper, we show leafwise cohomological expression of dynamical zeta function on a Riemannian foliated dynamical system. …

    数理解析研究所講究録 (2162), 22-33, 2020-07

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  • Robot control by compliance distribution optimization on Riemannian manifolds  [in Japanese]

    ISHIGAKI Taiki , YAMAMOTO Ko , NAKAMURA Yoshihiko

    … To evaluate the distance between matrices, we use Riemannian geodesic distance that allows us to consider the geometric structure of positive definite symmetric matrix. …

    The Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2020(0), 2A2-G13, 2020

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  • Heat trace asymptotics on equiregular sub-Riemannian manifolds

    Inahama Yuzuru , Taniguchi Setsuo

    … <p>We study a "div-grad type" sub-Laplacian with respect to a smooth measure and its associated heat semigroup on a compact equiregular sub-Riemannian manifold. … Our main result holds true for any smooth measure on the manifold, but it has a spectral geometric meaning when Popp's measure is considered. …

    Journal of the Mathematical Society of Japan 72(4), 1049-1096, 2020

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  • Differentiable sphere theorems whose comparison spaces are standard spheres or exotic ones

    Kondo Kei , Tanaka Minoru

    … <p>We show that for an arbitrarily given closed Riemannian manifold <i>M</i> … with a single cut point, every closed Riemannian manifold <i>N</i> …

    Kodai Mathematical Journal 43(2), 349-365, 2020

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  • Monotonicity of eigenvalues of the <i>p</i>-Laplace operator under the Ricci-Bourguignon flow

    Dung Ha Tuan

    … <p>Given a compact Riemannian manifold without boundary, in this paper, we discuss the monotonicity of the first eigenvalue of the <i>p</i>-Laplace operator under the Ricci-Bourguignon flow. …

    Kodai Mathematical Journal 43(1), 143-161, 2020

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  • Realizing the Teichmuller space as a symplectic quotient

    Diez Tobias , Ratiu Tudor S.

    … Given a closed surface endowed with a volume form, we equip the space of compatible Riemannian structures with the structure of an infinite-dimensional symplectic manifold. … We show that the natural action of the group of volumepreserving diffeomorphisms by push-forward has a group-valued momentum map that assigns to a Riemannian metric the canonical bundle. …

    数理解析研究所講究録 (2137), 60-67, 2019-12

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  • The constrained total variation flow (Theoretical Developments to Phenomenon Analyses based on Nonlinear Evolution Equations)

    Moll Salvador

    In this paper we review some recent results about the total variation flow for functions into manifolds. After recalling some well-know results about existence, uniqueness and qualitative properties f …

    数理解析研究所講究録 (2121), 111-128, 2019-07

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  • Theory of Elasticity on Riemannian Manifolds and Its Application to Inhomogeneous Deformation  [in Japanese]

    TANJI Daiki , TARUMI Ryuichi , KOBAYASHI Shunsuke , HORIKAWA Yuto

    … Our formulation is based on the nonlinear elasticity on Riemannian manifold. … The dilatational deformation is expressed by Riemannian metric tensor <i>g</i><sub>[0]</sub> … Elastic deformation, which is understood as an embedding mapping from the manifold to Euclidean space R<sup>2</sup>, is determined so as to minimize the strain energy density under suitable boundary conditions. …

    The Proceedings of The Computational Mechanics Conference 2019.32(0), 125, 2019

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  • ON RIEMANNIAN MANIFOLDS WITH POSITIVE WEIGHTED RICCI CURVATURE OF NEGATIVE EFFECTIVE DIMENSION

    Hung MAI Cong

    … <p>In this paper, we investigate complete Riemannian manifolds satisfying the lower weighted Ricci curvature bound Ric<i><sub>N</sub></i> … −</i>1 and the minimum is attained, then the manifold splits off the real line as a warped product of hyperbolic nature.</p> …

    Kyushu Journal of Mathematics 73(1), 205-218, 2019

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  • Existence and non-existence of caloric morphisms with Bateman space-mapping for radial metrics

    Shimomura Katsunori

    <p>In semi-euclidean spaces, conformal mappings are consists of similarities, inversions, and Bateman mapping [14]. In this note, we shall discuss problems whether there exist caloric morphisms …

    Mathematical Journal of Ibaraki University 51(0), 1-12, 2019

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  • Gluing construction of compact Spin(7)-manifolds

    Doi Mamoru , Yotsutani Naoto

    … ∖ 𝐷<sub>2</sub>)/⟨𝜎<sub>2</sub>⟩ together to obtain a compact Riemannian 8-manifold (𝑀, 𝑔) whose holonomy group Hol(𝑔) is contained in Spin(7). … Furthermore, if the \widehat{𝐴}-genus of 𝑀 equals 1, then 𝑀 is a compact Spin(7)-manifold, i.e. a compact Riemannian manifold with holonomy Spin(7).</p> …

    Journal of the Mathematical Society of Japan 71(2), 349-382, 2019

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  • Some remarks on Riemannian manifolds with parallel Cotton tensor

    Fu Hai-Ping , Xu Gao-Bo , Tao Yong-Qian

    … <p>We give some sufficient conditions for stochastically complete Riemannian manifolds with parallel Cotton tensor to be either Einstein or of constant sectional curvature, and obtain an optimal pinching theorem. …

    Kodai Mathematical Journal 42(1), 64-74, 2019

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  • Hermitian Tanno Connection and Bochner Type Curvature Tensors of Contact Riemannian Manifolds

    Nagase Masayoshi , Sasaki Daisuke

    … On a contact Riemannian manifold, considering the curvature of hermitian Tanno connection, we introduce Bochner type curvature tensors. …

    Journal of Mathematical Sciences The University of Tokyo 25(2), 149-169, 2018-06-29

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  • BIHARMONIC SUBMANIFOLDS IN A RIEMANNIAN MANIFOLD

    Koiso Norihito , Urakawa Hajime

    In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of the Euclidean space …

    Osaka Journal of Mathematics 55(2), 325-346, 2018-04

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  • Brachistochrone curve as a geodesic in a surface  [in Japanese]

    森田 正亮

    独立行政法人国立高等専門学校機構沖縄工業高等専門学校紀要 (12), 37-45, 2018-03

  • GEOMETRY OF GEODESIC SPHERES IN A COMPLEX PROJECTIVE SPACE IN TERMS OF THEIR GEODESICS

    Maeda Sadahiro

    … Geodesic spheres G(r) are fundamental examples of (real) hypersurfaces in a Riemannian manifold. …

    Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics (51), 1-5, 2018-03

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  • Brachistochrone curve as a geodesic in a surface  [in Japanese]

    森田 正亮 , もりた まさあき , Morita Masaaki , 沖縄工業高等専門学校 総合科学科

    粒子がポテンシャル中を運動するときに,ある二点間を最短時間で結ぶ「最速降下曲線」を曲面上の測地線と見なすことはできるか?という問題について考察する.共形平坦な計量を持つ2次元リーマン多様体での測地線と見なせることは直ちに分かるが,その多様体を3次元空間R^3に埋め込むことができるかどうかは自明でない.そこで,回転面という条件の下で曲面を構成することを試み,ポテンシャルと構成された曲面の関係を明らか …

    沖縄工業高等専門学校紀要 = Bulletin of National Institute of Technology, Okinawa College (12), 37-45, 2018-03

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  • Riemannian Newton's Method on the Grassmann Manifold Exploiting the Quotient Structure  [in Japanese]

    Sato Hiroyuki , Aihara Kensuke

    <p><b>概要.</b> グラスマン多様体はシュティーフェル多様体の直交群による商多様体と見なすことができる.本論文では,そのような商多様体上の最適化問題を取り上げ,一般の目的関数に対して有効なニュートン法について議論する.特に,数値計算が行えるようにニュートン方程式を水平空間上の線形方程式として導出する.また,クリロフ部分空間法に基づき,目的関数のヘシアンの …

    Transactions of the Japan Society for Industrial and Applied Mathematics 28(4), 205-241, 2018

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