Research Article
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Year 2014, , 37 - 46, 30.10.2014
https://doi.org/10.36890/iejg.593981

Abstract

References

  • [1] Belkhelfa, M., Dillen, F. and Inoguchi, J.-I., Surfaces with parallel second fundamental form in Bianchi-Cartan-Vranceanu spaces, in ”PDEs, submanifolds and affine differential geometry” (Warsaw, 2000), 67-87, Banach Center Publ., 57, Polish Acad. Sci., Warsaw, 2002.
  • [2] Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Second edition.Progress in Mathematics, 203. Birkh¨auser Boston, Inc., Boston, MA, 2010.
  • [3] Caddeo, R., Montaldo, S., Oniciuc, C. and Piu, P., The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional spaces, in ”Modern trends in geometry and topology”, 121-131, Cluj Univ. Press, Cluj-Napoca, 2006.
  • [4] Calvaruso, G., Three-dimensional homogeneous almost contact metric structures, J. Geom. Phys., 69(2013), 60-73.
  • [5] Chern S. S. and Hamilton, R. S., On Riemannian metrics adapted to three-dimensional contact manifolds, With an appendix by Alan Weinstein. Lecture Notes in Math., 1111, Workshop Bonn 1984, 279-308, Springer, Berlin, 1985.
  • [6] Cho, J. T., Inoguchi J.-I. and Lee, J.-E., On slant curves in Sasakian 3-manifolds, Bull. Austral. Math. Soc., 74(2006), no. 3, 359-367.
  • [7] Cho, J. T. and Kon, M., The Tanaka-Webster connection and real hypersurfaces in a complex space form, Kodai Math. J., 34(2011), no. 3, 474-484.
  • [8] Chow, B., Lu, P. and Ni, L., Hamilton’s Ricci flow, Graduate Studies in Mathematics, 77, American Mathematical Society, Providence, RI; Science Press, New York, 2006.
  • [9] Dragomir, S. and Perrone, D., Harmonic vector fields. Variational principles and differential geometry, Amsterdam, Elsevier, 2012.
  • [10] Fastenakels, J., Munteanu, M. I. and Van Der Veken, J., Constant angle surfaces in the Heisenberg group, Acta Math. Sin. (Engl. Ser.), 27(2011), no. 4, 747-756.
  • [11] Lee, H., Extensions of the duality between minimal surfaces and maximal surfaces, Geom. Dedicata, 151(2011), 373-386.
  • [12] McMullen, C. T., The evolution of geometric structures on 3-manifolds, Bull. Amer. Math. Soc., 48(2011), no. 2, 259-274.
  • [13] Milnor, J., Curvatures of left invariant metrics on Lie groups, Advances in Math., 21(1976), no. 3, 293-329.
  • [14] Nicolaescu, L. I., Adiabatic limits of the Seiberg-Witten equations on Seifert manifolds, Comm. Anal. Geom., 6(1998), no. 2, 331-392.
  • [15] Ou, Y.-L. and Wang, Z.-P., Constant mean curvature and totally umbilical biharmonic sur- faces in 3-dimensional geometries, J. Geom. Phys., 61(2011), no. 10, 1845-1853.
  • [16] Perrone, D., Homogeneous contact Riemannian three-manifolds, Illinois J. Math., 42 (1998), no. 2, 243-256.
  • [17] Van der Veken, J., Higher order parallel surfaces in Bianchi-Cartan-Vranceanu spaces, Results Math., 51(2008) no. 3-4 339-359.

ADAPTED METRICS AND WEBSTER CURVATURE ON THREE CLASSES OF 3-DIMENSIONAL GEOMETRIES

Year 2014, , 37 - 46, 30.10.2014
https://doi.org/10.36890/iejg.593981

Abstract


References

  • [1] Belkhelfa, M., Dillen, F. and Inoguchi, J.-I., Surfaces with parallel second fundamental form in Bianchi-Cartan-Vranceanu spaces, in ”PDEs, submanifolds and affine differential geometry” (Warsaw, 2000), 67-87, Banach Center Publ., 57, Polish Acad. Sci., Warsaw, 2002.
  • [2] Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Second edition.Progress in Mathematics, 203. Birkh¨auser Boston, Inc., Boston, MA, 2010.
  • [3] Caddeo, R., Montaldo, S., Oniciuc, C. and Piu, P., The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional spaces, in ”Modern trends in geometry and topology”, 121-131, Cluj Univ. Press, Cluj-Napoca, 2006.
  • [4] Calvaruso, G., Three-dimensional homogeneous almost contact metric structures, J. Geom. Phys., 69(2013), 60-73.
  • [5] Chern S. S. and Hamilton, R. S., On Riemannian metrics adapted to three-dimensional contact manifolds, With an appendix by Alan Weinstein. Lecture Notes in Math., 1111, Workshop Bonn 1984, 279-308, Springer, Berlin, 1985.
  • [6] Cho, J. T., Inoguchi J.-I. and Lee, J.-E., On slant curves in Sasakian 3-manifolds, Bull. Austral. Math. Soc., 74(2006), no. 3, 359-367.
  • [7] Cho, J. T. and Kon, M., The Tanaka-Webster connection and real hypersurfaces in a complex space form, Kodai Math. J., 34(2011), no. 3, 474-484.
  • [8] Chow, B., Lu, P. and Ni, L., Hamilton’s Ricci flow, Graduate Studies in Mathematics, 77, American Mathematical Society, Providence, RI; Science Press, New York, 2006.
  • [9] Dragomir, S. and Perrone, D., Harmonic vector fields. Variational principles and differential geometry, Amsterdam, Elsevier, 2012.
  • [10] Fastenakels, J., Munteanu, M. I. and Van Der Veken, J., Constant angle surfaces in the Heisenberg group, Acta Math. Sin. (Engl. Ser.), 27(2011), no. 4, 747-756.
  • [11] Lee, H., Extensions of the duality between minimal surfaces and maximal surfaces, Geom. Dedicata, 151(2011), 373-386.
  • [12] McMullen, C. T., The evolution of geometric structures on 3-manifolds, Bull. Amer. Math. Soc., 48(2011), no. 2, 259-274.
  • [13] Milnor, J., Curvatures of left invariant metrics on Lie groups, Advances in Math., 21(1976), no. 3, 293-329.
  • [14] Nicolaescu, L. I., Adiabatic limits of the Seiberg-Witten equations on Seifert manifolds, Comm. Anal. Geom., 6(1998), no. 2, 331-392.
  • [15] Ou, Y.-L. and Wang, Z.-P., Constant mean curvature and totally umbilical biharmonic sur- faces in 3-dimensional geometries, J. Geom. Phys., 61(2011), no. 10, 1845-1853.
  • [16] Perrone, D., Homogeneous contact Riemannian three-manifolds, Illinois J. Math., 42 (1998), no. 2, 243-256.
  • [17] Van der Veken, J., Higher order parallel surfaces in Bianchi-Cartan-Vranceanu spaces, Results Math., 51(2008) no. 3-4 339-359.
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Mircea Crasmareanu

Publication Date October 30, 2014
Published in Issue Year 2014

Cite

APA Crasmareanu, M. (2014). ADAPTED METRICS AND WEBSTER CURVATURE ON THREE CLASSES OF 3-DIMENSIONAL GEOMETRIES. International Electronic Journal of Geometry, 7(2), 37-46. https://doi.org/10.36890/iejg.593981
AMA Crasmareanu M. ADAPTED METRICS AND WEBSTER CURVATURE ON THREE CLASSES OF 3-DIMENSIONAL GEOMETRIES. Int. Electron. J. Geom. October 2014;7(2):37-46. doi:10.36890/iejg.593981
Chicago Crasmareanu, Mircea. “ADAPTED METRICS AND WEBSTER CURVATURE ON THREE CLASSES OF 3-DIMENSIONAL GEOMETRIES”. International Electronic Journal of Geometry 7, no. 2 (October 2014): 37-46. https://doi.org/10.36890/iejg.593981.
EndNote Crasmareanu M (October 1, 2014) ADAPTED METRICS AND WEBSTER CURVATURE ON THREE CLASSES OF 3-DIMENSIONAL GEOMETRIES. International Electronic Journal of Geometry 7 2 37–46.
IEEE M. Crasmareanu, “ADAPTED METRICS AND WEBSTER CURVATURE ON THREE CLASSES OF 3-DIMENSIONAL GEOMETRIES”, Int. Electron. J. Geom., vol. 7, no. 2, pp. 37–46, 2014, doi: 10.36890/iejg.593981.
ISNAD Crasmareanu, Mircea. “ADAPTED METRICS AND WEBSTER CURVATURE ON THREE CLASSES OF 3-DIMENSIONAL GEOMETRIES”. International Electronic Journal of Geometry 7/2 (October 2014), 37-46. https://doi.org/10.36890/iejg.593981.
JAMA Crasmareanu M. ADAPTED METRICS AND WEBSTER CURVATURE ON THREE CLASSES OF 3-DIMENSIONAL GEOMETRIES. Int. Electron. J. Geom. 2014;7:37–46.
MLA Crasmareanu, Mircea. “ADAPTED METRICS AND WEBSTER CURVATURE ON THREE CLASSES OF 3-DIMENSIONAL GEOMETRIES”. International Electronic Journal of Geometry, vol. 7, no. 2, 2014, pp. 37-46, doi:10.36890/iejg.593981.
Vancouver Crasmareanu M. ADAPTED METRICS AND WEBSTER CURVATURE ON THREE CLASSES OF 3-DIMENSIONAL GEOMETRIES. Int. Electron. J. Geom. 2014;7(2):37-46.