본문 바로가기
KERD
논문KCI 등재

On generalized quasi-conformal $N(k,\mu )$-manifolds

Kanak Kanti Baishya|Partha Roy Chowdhury
대한수학회 (The Korean Mathematical Society)|2016.01|대한수학회논문집 (Communications of the KMS)|제31권 제1호|pp. 163-176

2

조회

0

다운로드

5

인용

0

참고문헌

키워드

generalized quasi-conformal curvature tensor$N(k\mu )$-manifold$\eta $-Einsteinsemi-symmetricRicci semi-symmetric
주제분류수학

초록

The object of the present paper is to introduce a new curvature tensor, named \textit{generalized quasi-conformal curvature tensor} which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of \textit{generalized quasi-conformal curvature tensor} are studied in the frame of $(k,\mu )$-contact metric manifolds.

Abstract

The object of the present paper is to introduce a new curvature tensor, named \textit{generalized quasi-conformal curvature tensor} which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of \textit{generalized quasi-conformal curvature tensor} are studied in the frame of $(k,\mu )$-contact metric manifolds.

참고문헌 (28)

  1. Ch. Baikoussis, "On a type of contact manifolds", J. Geom, 46(1-2), pp.1~9 (1993)
  2. D. E. Blair, "Contact Manifolds in Riemannian Geometry", Lecture Notes in Math, 509 (1976), Springer-Verlag
  3. D. E. Blair, "Two remarks on contact metric structures", Tohoku Math. J. (2), 29(3), pp.319~324 (1977)
  4. D. E. Blair, "Contact metric manifolds satisfying a nullity condition", Israel J. Math, 19(1-3), pp.189~214 (1995)
  5. E. Boeckx, "A full classification of contact metric (k, μ)-spaces", Illinois J. Math, 44(1), pp.212~219 (2000)
  6. E. Cartan, "Sur une Classe Remarquable d’espaces de Riemannian", Bull. Soc. Math. France, 54, pp.214~264 (1926)
  7. R. Deszcz, "Some examples of nonsemisymmetric Ricci-semi-symmetric hypersurfaces", Colloq. Math, 94(1), pp.87~101 (2002)
  8. L. P. Eisenhart, "Riemannian Geometry" (1949), Princeton University Press
  9. Y. Ishii, "On conharmonic transformations", Tensor (N.S.), 7, pp.73~80 (1957)
  10. O. Kowalski, "An explicit classification of three dimensional Riemannian spaces satisfy-ing R(X, Y ) · R = 0", Czechoslovak Math. J, 46(3), pp.427~474 (1996)
  11. K. Nomizu, "On the decomposition of generalized curvature tensor fields, Differential geometry (in honor of Kentaro Yano)", pp.335~345 (1972), Kinokuniya
  12. M. Okumura, "Some remarks on space with a certain contact structure", Tohoku Math. J. (2), 14, pp.135~145 (1962)
  13. B. J. Papantoniou, "Contact Riemannian manifolds satisfying R(ξ,X) · R = 0 and ξ∈(k, μ)-nullity distribution", Yokohama Math. J, 40(2), pp.149~161 (1993)
  14. D. Perrone, "Contact Riemannian manifolds satisfying R(ξ,X)·R = 0", Yokohama Math. J, 39(2), pp.141~149 (1992)
  15. G. P. Pokhariyal, "Curvatur tensors and their relativistics significance", Yokohama Math. J, 18, pp.105~108 (1970)
  16. A. Sarkar, "On the quasi conformal curvature tensor of a (k, μ)-contact metric manifold", Math. Rep. (Bucur.), 14(2), pp.115~129 (2012)
  17. S. Sasaki, "Almost-contact manifolds Part I Lecture Notes" (1965), Mathematical Institue, Tohoku University
  18. K. Sekigawa, "Sufficient condition for a Riemannian manifold to be locally symmetric", Pacific J. Math, 34, pp.157~162 (1970)
  19. A. A. Shaikh, "On 3-dimensional generalized (k, μ)-contact manifolds", Balkan J. Geom. Appl, 12(1), pp.122~134 (2007)
  20. A. A. Shaikh, "On (k, μ)-contact metric manifolds", An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 51(2), pp.405~416 (2005)
  21. A. A. Shaikh, "On (k, μ)-contact metric manifolds", Differ. Geom. Dyn. Syst, 8, pp.253~261 (2006)
  22. Z. I. Szabo, "Structure Theorems on Riemannian spaces satisfying R(X, Y ) ·R = 0. I", J. Differential Geom, 17(4), pp.531~582 (1982)
  23. Z. I. Szabo, "Classification and construction of complete hypersurfaces satisfying R(X, Y ) ·R = 0.", Acta Sci. Math. (Szeged), 47(3-4), pp.321~348 (1984)
  24. Z. I. Szabo, "Structure theorems on Riemannian spaces satisfying R(X, Y )·R = 0. II", Geom. Dedicata, 19(1), pp.65~108 (1985)
  25. S. Tanno, "Ricci curvatures of contact Riemannian manifolds", Tohoku Math. J. (2), 40(3), pp.441~448 (1988)
  26. K. Yano, "Curvature and Betti Numbers", Ann. of Math. Stud, 32 (1953), Princeton University Press
  27. K. Yano, "Riemannian manifolds admitting a conformal transformation group", J. Differential Geom, 2, pp.161~184 (1968)
  28. Ahmet Yildiz, "A CLASSIFICATION OF (κ, μ)-CONTACT METRIC MANIFOLDS", 대한수학회논문집, 27(2), pp.327~339 (2012), 대한수학회

관련 논문AI추천

ON CONFORMAL AND QUASI-CONFORMAL CURVATURE TENSORS OF AN N(k)-QUASI EINSTEIN MANIFOLDAbolfazl Taleshian, Aliakbar Hosseinzadeh대한수학회 · 대한수학회논문집2012 · 제27권 제2호Certain semisymmetry properties of $(\kappa,\;\mu)$-contact metric manifoldsJae Bok Jun, Srimayee Samui, Uday Chand De대한수학회 · 대한수학회보2016 · 제53권 제4호QUASI-CONFORMAL CURVATURE TENSOR ON N (k)-QUASI EINSTEIN MANIFOLDSAvijit Sarkar, Dipankar Hazra강원경기수학회 · 한국수학논문집2021 · 제29권 제4호A CLASSIFICATION OF (κ, μ)-CONTACT METRIC MANIFOLDSAhmet Yildiz, Uday Chand De대한수학회 · 대한수학회논문집2012 · 제27권 제2호ON A CLASS OF GENERALIZED (k, μ)-CONTACT METRIC MANIFOLDSSujit Ghosh, Uday Chand De장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2010 · 제13권 제3호Sasakian manifolds with quasi-conformal curvature tensor전재복, Abul Kalam Gazi, Uday Chand De대한수학회 · 대한수학회보2008 · 제45권 제2호

이 간행물의 다른 논문 (15건)

A note on the modified $k$-Fibonacci-like sequence권영우pp. 1-16Hesitant fuzzy semigroups with two frontiersChul Hwan Park, Young Bae Jun, Kyoung Ja Leepp. 17-25Codes based on residuated latticesSEOK-ZUN SONG, Tsafack Surdive Atamewoue, YOUNG BAE JUN, CELESTIN LELE, Selestin Ndjeyapp. 27-40On generalized zero-difference balanced functionsQunying Liao, Lin Jiangpp. 41-52Generalization of the Fej\'{e}r--Hadamard's inequality for convex function on coordinatesAtiq Ur Rehman, Ghulam Faridpp. 53-64
원문 보기