• 제목/요약/키워드: Riemannian

검색결과 543건 처리시간 0.02초

HYPERSURFACES OF ALMOST γ-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH SEMI-SYMMETRIC METRIC CONNECTION

  • Jun, Jae-Bok;Ahmad, Mobin
    • 대한수학회보
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    • 제46권5호
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    • pp.895-903
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    • 2009
  • We define a semi-symmetric metric connection in an almost $\gamma$-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost $\gamma$-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.

EMBEDDING RIEMANNIAN MANIFOLDS VIA THEIR EIGENFUNCTIONS AND THEIR HEAT KERNEL

  • Abdalla, Hiba
    • 대한수학회보
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    • 제49권5호
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    • pp.939-947
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    • 2012
  • In this paper, we give a generalization of the embeddings of Riemannian manifolds via their heat kernel and via a finite number of eigenfunctions. More precisely, we embed a family of Riemannian manifolds endowed with a time-dependent metric analytic in time into a Hilbert space via a finite number of eigenfunctions of the corresponding Laplacian. If furthermore the volume form on the manifold is constant with time, then we can construct an embedding with a complete eigenfunctions basis.

A NEW CLASS OF RIEMANNIAN METRICS ON TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD

  • Baghban, Amir;Sababe, Saeed Hashemi
    • 대한수학회논문집
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    • 제35권4호
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    • pp.1255-1267
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    • 2020
  • The class of isotropic almost complex structures, J𝛿,𝜎, define a class of Riemannian metrics, g𝛿,𝜎, on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics g𝛿,0 using the geometry of tangent bundle. As a by-product, some integrability results will be reported for J𝛿,𝜎.

FIBRED RIEMANNIAN SPACE WITH ALMOST COMPLEX STRUCTURES

  • Choi, Jin-Hyuk;Kang, Il-Won;Kim, Byung-Hak;Shin, Yang-Mi
    • 대한수학회지
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    • 제46권1호
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    • pp.171-185
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    • 2009
  • We study fibred Riemannian spaces with almost complex structures which are induced by the almost complex structure or the almost contact structure on the base and fibre. We show that if the total space is a complex space form, then the total space is locally Euclidean. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structures.

OPTION PRICING UNDER GENERAL GEOMETRIC RIEMANNIAN BROWNIAN MOTIONS

  • Zhang, Yong-Chao
    • 대한수학회보
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    • 제53권5호
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    • pp.1411-1425
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    • 2016
  • We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Shin, Jong Moon
    • East Asian mathematical journal
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    • 제31권1호
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    • pp.33-40
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    • 2015
  • We study the geometry of r-lightlike submanifolds M of a semi-Riemannian manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (a) the screen distribution of M is totally geodesic in M, and (b) at least one among the r-th lightlike second fundamental forms is parallel with respect to the induced connection of M. The main result is a classification theorem for irrotational r-lightlike submanifold of a semi-Riemannian manifold of index r admitting a semi-symmetric non-metric connection.

SPACES OF CONFORMAL VECTOR FIELDS ON PSEUDO-RIEMANNIAN MANIFOLDS

  • KIM DONG-SOO;KIM YOUNG-HO
    • 대한수학회지
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    • 제42권3호
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    • pp.471-484
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    • 2005
  • We study Riemannian or pseudo-Riemannian manifolds which carry the space of closed conformal vector fields of at least 2-dimension. Subject to the condition that at each point the set of closed conformal vector fields spans a non-degenerate subspace of the tangent space at the point, we prove a global and a local classification theorems for such manifolds.

NORMAL HOLONOMY GROUP OF A RIEMANNIAN FOLIATIO $N^*$

  • Pak, Hong-Kyung;Pak, Jin-Suk
    • 대한수학회보
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    • 제30권1호
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    • pp.17-23
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    • 1993
  • In this paper, we will discuss on the above problem for the case that .upsilon. is a Riemannian foliation. If .upsilon. is a Riemannian foliation on (M, g), we derive some basic relations between the curvature $R^{D}$ of the normal connection D and the curvature R of the Levi-Civita connection .del. on (M, g) (see Lemma 1).).

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SUBMANIFOLDS OF AN ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH A QUARTER-SYMMETRIC NON-METRIC CONNECTION

  • Ahmad, Mobin;Jun, Jae-Bok;Haseeb, Abdul
    • 충청수학회지
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    • 제24권1호
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    • pp.91-104
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    • 2011
  • We define a quarter-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider the submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter-symmetric non-metric connection. We also obtain the Gauss, Codazzi and Weingarten equations and the curvature tensor for the submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter-symmetric non-metric connection.

RIEMANNIAN MANIFOLDS WITH A SEMI-SYMMETRIC METRIC P-CONNECTION

  • Chaubey, Sudhakar Kr;Lee, Jae Won;Yadav, Sunil Kr
    • 대한수학회지
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    • 제56권4호
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    • pp.1113-1129
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    • 2019
  • We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.