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

Yıl 2014, Cilt: 7 Sayı: 2, 37 - 46, 30.10.2014

Mircea Crasmareanu

https://doi.org/10.36890/iejg.593981

Cited By: 3

Öz

Anahtar Kelimeler

Webster curvature, unimodular Lie group, Milnor frame, Bianchi-Cartan-Vranceanu metric, warped metric

Kaynakça

• [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.