Research Article
Year 2020,
Volume: 2 Issue: 1, 22 - 30, 04.03.2020
Abstract
References
- \bibitem{BAR} C. B\"ar , \textit{Real Killing spinors and holonomy}, Comm. Math. Phys., \textbf{154} (1993), 509-521.
- \bibitem{BB} G. Beldjilali, M. Belkhelfa, {\it K\"ahlerian structures on $\mathcal{D}$-homothetic bi-warping}, JGSP {\bf 42} (2016) 1-13.
- \bibitem{BB2} G. Beldjilali , M. Belkhelfa , {\it K\"ahlerian structures on generalized doubly $\mathcal{D}$-homothetic bi-warping}, African Diaspora Journal of Mathematics, Vol. {\bf 21} N. 2 (2018) 1-14.
- \bibitem{CHE} B. Y. Chen, {\it Geometry of submanifolds}, Marcel Dekker. Ine. New York, 1973.
- \bibitem{BL1} D. E. Blair , {\it Contact Manifolds in Riemannian Geometry}, 17-35, Lecture Nots in Mathematics 509, Springer, 1976.
- \bibitem{BL2} D. E. Blair, {\it Riemannian Geometry of Contact and Symplectic Manifolds}, Progress in Mathematics Vol. {\bf 203}, Birhauser, Boston, 2002.
- \bibitem{BL3} D. E. Blair, J. A. Oubi$\tilde{n}$a, {\it Conformal and related changes of metric on the product of two almost contact metric manifolds}, Publ. Mat. {\bf 34} (1), 199-207 (1990).
- \bibitem{BL5} D. E. Blair , {\it $\mathcal{D}$-homothetic warping}, Publications de l'institut mathématique, Nouvelle série, tome {\bf 94} (108) , 47-54 (2013).
- \bibitem{CAL} E. Calabi {\it M\'{e}triques k\"{a}hl\'{e}riennes et fibr\'{e}s holomorphes}, Ann. Scient. Ec. Norm.Sup., {\bf 12}(1979), pp. 269-294.
- \bibitem{OUB} J.A. Oubi$\tilde{n}$a, {\it New classes of almost contact metric structures}, Publicationes Mathematicae, Debrecen, {\bf 32}, 187-193 (1985).
- \bibitem{TAN} S. Tanno, {\it The topology of contact Riemannian manifolds}, Illinois J. Math. {\bf 12} (1968), 700-717.
- \bibitem{TA2} S. Tanno, {\it Partially conformal transformations with respect to $(m-1)$-dimensional distribution of $m$-dimensional Riemannian manifolds}, Tohoku Math. J. 1965. {\bf 2}, 17. P. 358-409.
- \bibitem{TM} T. Tshikuna-Matamba, {\it Quelques classes des vari\'et\'es m\'etriques \`a 3-structures presque de contact}, Annals of University of Craiova, Math. Comp. Sci. Ser. Volume {\bf 31}, 2004, Pages 94-101
- \bibitem{WY1} Y. Watanabe, {\it Almost Hermitian and K\"{a}hler structures on product manifolds}, Proc of the Thirteenth International Workshop on Diff. Geom. {\bf 13}, (2009) 1-16.
- \bibitem{WY2} Y. Watanabe, M. Hiroshi, {\it From Sasakian 3-structures to quaternionic geometry}, Archivum Mathematicum, {\bf 34} (1998), 379-386. \bibitem{YK} K. Yano and M. Kon, {\it Structures on Manifolds}, Series in Pure Math., Vol {\bf 3}, World Sci.,1984.
Year 2020,
Volume: 2 Issue: 1, 22 - 30, 04.03.2020
Abstract
We introduce the notion of $\mathcal{D}$-isometric warping and prove some basic properties. We give an application to some questions of the characterization of certain geometric structures. Firstly, we construct a $1$-parameter family of K\"ahlerian structures from a single Sasakian structure with a concrete example. Secondly, we build a quaternionic K\"ahlerian structure from a $3$-Sasakian structures.
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References
- \bibitem{BAR} C. B\"ar , \textit{Real Killing spinors and holonomy}, Comm. Math. Phys., \textbf{154} (1993), 509-521.
- \bibitem{BB} G. Beldjilali, M. Belkhelfa, {\it K\"ahlerian structures on $\mathcal{D}$-homothetic bi-warping}, JGSP {\bf 42} (2016) 1-13.
- \bibitem{BB2} G. Beldjilali , M. Belkhelfa , {\it K\"ahlerian structures on generalized doubly $\mathcal{D}$-homothetic bi-warping}, African Diaspora Journal of Mathematics, Vol. {\bf 21} N. 2 (2018) 1-14.
- \bibitem{CHE} B. Y. Chen, {\it Geometry of submanifolds}, Marcel Dekker. Ine. New York, 1973.
- \bibitem{BL1} D. E. Blair , {\it Contact Manifolds in Riemannian Geometry}, 17-35, Lecture Nots in Mathematics 509, Springer, 1976.
- \bibitem{BL2} D. E. Blair, {\it Riemannian Geometry of Contact and Symplectic Manifolds}, Progress in Mathematics Vol. {\bf 203}, Birhauser, Boston, 2002.
- \bibitem{BL3} D. E. Blair, J. A. Oubi$\tilde{n}$a, {\it Conformal and related changes of metric on the product of two almost contact metric manifolds}, Publ. Mat. {\bf 34} (1), 199-207 (1990).
- \bibitem{BL5} D. E. Blair , {\it $\mathcal{D}$-homothetic warping}, Publications de l'institut mathématique, Nouvelle série, tome {\bf 94} (108) , 47-54 (2013).
- \bibitem{CAL} E. Calabi {\it M\'{e}triques k\"{a}hl\'{e}riennes et fibr\'{e}s holomorphes}, Ann. Scient. Ec. Norm.Sup., {\bf 12}(1979), pp. 269-294.
- \bibitem{OUB} J.A. Oubi$\tilde{n}$a, {\it New classes of almost contact metric structures}, Publicationes Mathematicae, Debrecen, {\bf 32}, 187-193 (1985).
- \bibitem{TAN} S. Tanno, {\it The topology of contact Riemannian manifolds}, Illinois J. Math. {\bf 12} (1968), 700-717.
- \bibitem{TA2} S. Tanno, {\it Partially conformal transformations with respect to $(m-1)$-dimensional distribution of $m$-dimensional Riemannian manifolds}, Tohoku Math. J. 1965. {\bf 2}, 17. P. 358-409.
- \bibitem{TM} T. Tshikuna-Matamba, {\it Quelques classes des vari\'et\'es m\'etriques \`a 3-structures presque de contact}, Annals of University of Craiova, Math. Comp. Sci. Ser. Volume {\bf 31}, 2004, Pages 94-101
- \bibitem{WY1} Y. Watanabe, {\it Almost Hermitian and K\"{a}hler structures on product manifolds}, Proc of the Thirteenth International Workshop on Diff. Geom. {\bf 13}, (2009) 1-16.
- \bibitem{WY2} Y. Watanabe, M. Hiroshi, {\it From Sasakian 3-structures to quaternionic geometry}, Archivum Mathematicum, {\bf 34} (1998), 379-386. \bibitem{YK} K. Yano and M. Kon, {\it Structures on Manifolds}, Series in Pure Math., Vol {\bf 3}, World Sci.,1984.
There are 15 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | March 4, 2020 |
| Published in Issue | Year 2020 Volume: 2 Issue: 1 |
