Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
Riemannian map; semi-slant Riemannian map; harmonic map; totally geodesic map
Riemannian map; semi-slant Riemannian map; harmonic map; totally geodesic map
Summary:
We introduce semi-slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of semi-slant immersions, invariant Riemannian maps, anti-invariant Riemannian maps and slant Riemannian maps. We obtain characterizations, investigate the harmonicity of such maps and find necessary and sufficient conditions for semi-slant Riemannian maps to be totally geodesic. Then we relate the notion of semi-slant Riemannian maps to the notion of pseudo-horizontally weakly conformal maps, which are useful for proving various complex-analytic properties of stable harmonic maps from complex projective space and give many examples of such maps.
References:
[1] Abraham, R., Marsden, J. E., Ratiu, T.: Manifolds, Tensor Analysis, and Applications (2nd edition). Applied Mathematical Sciences 75 Springer, New York (1988). DOI 10.1007/978-1-4612-1029-0 | MR 0960687
[2] Aprodu, M. A., Aprodu, M.: Implicitly defined harmonic PHH submersions. Manuscr. Math. 100 (1999), 103-121. DOI 10.1007/s002290050198 | MR 1714452 | Zbl 0938.53035
[3] Aprodu, M. A., Aprodu, M., Brînzănescu, V.: A class of harmonic submersions and minimal submanifolds. Int. J. Math. 11 (2000), 1177-1191. DOI 10.1142/S0129167X0000057X | MR 1809307 | Zbl 0978.58006
[4] Baird, P., Wood, J. C.: Harmonic Morphisms Between Riemannian Manifolds. London Mathematical Society Monographs. New Series 29 Clarendon Press, Oxford University Press, Oxford (2003). MR 2044031 | Zbl 1055.53049
[5] Bejancu, A.: Geometry of CR-Submanifolds. Mathematics and Its Applications (East European Series) 23 D. Reidel Publishing Co., Dordrecht (1986). MR 0861408 | Zbl 0605.53001
[6] Burns, D., Burstall, F., Bartolomeis, P. de, Rawnsley, J.: Stability of harmonic maps of Kähler manifolds. J. Differ. Geom. 30 (1989), 579-594. DOI 10.4310/jdg/1214443603 | MR 1010173 | Zbl 0678.53062
[7] Candelas, P., Horowitz, G. T., Strominger, A., Witten, E.: Vacuum configurations for superstrings. Nuclear Phys. B (electronic only) 258 (1985), 46-74. MR 0800347
[8] Chen, B.-Y.: Geometry of Slant Submanifolds. Katholieke Universiteit Leuven, Dept. of Mathematics, Leuven (1990). MR 1099374 | Zbl 0716.53006
[9] Chen, B.-Y.: Slant immersions. Bull. Aust. Math. Soc. 41 (1990), 135-147. DOI 10.1017/S0004972700017925 | MR 1043974 | Zbl 0677.53060
[10] Chinea, D.: Almost contact metric submersions. Rend. Circ. Mat. Palermo (2) 34 (1985), 89-104. DOI 10.1007/BF02844887 | MR 0790818 | Zbl 0589.53041
[11] Eells, J. J., Sampson, J. H.: Harmonic mappings of Riemannian manifolds. Am. J. Math. 86 (1964), 109-160. DOI 10.2307/2373037 | MR 0164306 | Zbl 0122.40102
[12] Esposito, G.: From spinor geometry to complex general relativity. Int. J. Geom. Methods Mod. Phys. 2 (2005), 675-731. DOI 10.1142/S0219887805000752 | MR 2162076 | Zbl 1086.83025
[13] Falcitelli, M., Ianus, S., Pastore, A. M.: Riemannian Submersions and Related Topics. World Scientific, River Edge, New York (2004). MR 2110043 | Zbl 1067.53016
[14] Fischer, A. E.: Riemannian maps between Riemannian manifolds. Mathematical aspects of classical field theory. Proc. of the AMS-IMS-SIAM Joint Summer Research Conf., Seattle, Washington, USA, 1991 Contemp. Math. 132 American Mathematical Society, Providence (1992), 331-366 M. J. Gotay et al. DOI 10.1090/conm/132/1188447 | MR 1188447 | Zbl 0780.53033
[15] García-Río, E., Kupeli, D. N.: Semi-Riemannian Maps and Their Applications. Mathematics and Its Applications 475 Kluwer Academic Publishers, Dordrecht (1999). MR 1700746 | Zbl 0924.53003
[16] Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16 (1967), 715-737. MR 0205184 | Zbl 0147.21201
[17] Ianuş, S., Mazzocco, R., Vîlcu, G. E.: Riemannian submersions from quaternionic manifolds. Acta Appl. Math. 104 (2008), 83-89. DOI 10.1007/s10440-008-9241-3 | MR 2434668 | Zbl 1151.53329
[18] Lerner, D. E., eds., P. D. Sommers: Complex Manifold Techniques in Theoretical Physics. Research Notes in Mathematics 32 Pitman Advanced Publishing Program San Francisco (1979). MR 0564439 | Zbl 0407.00015
[19] Loubeau, E., Slobodeanu, R.: Eigenvalues of harmonic almost submersions. Geom. Dedicata 145 (2010), 103-126. DOI 10.1007/s10711-009-9409-7 | MR 2600948 | Zbl 1194.53055
[20] Marrero, J. C., Rocha, J.: Locally conformal Kähler submersions. Geom. Dedicata 52 (1994), 271-289. DOI 10.1007/BF01278477 | MR 1299880 | Zbl 0810.53054
[21] O'Neill, B.: The fundamental equations of a submersion. Mich. Math. J. 13 (1966), 459-469. DOI 10.1307/mmj/1028999604 | MR 0200865 | Zbl 0145.18602
[22] Papaghiuc, N.: Semi-slant submanifolds of a Kaehlerian manifold. An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 40 (1994), 55-61. MR 1328947 | Zbl 0847.53012
[23] Şahin, B.: Slant Riemannian maps to Kähler manifolds. Int. J. Geom. Methods Mod. Phys. 10 (2013), Paper No. 1250080, 12 pages. DOI 10.1142/S0219887812500806 | MR 3004125 | Zbl 1263.53025
[24] Şahin, B.: Semi-invariant Riemannian maps to Kähler manifolds. Int. J. Geom. Methods Mod. Phys. 8 (2011), 1439-1454. DOI 10.1142/S0219887811005725 | MR 2873816 | Zbl 1242.53039
[25] Şahin, B.: Invariant and anti-invariant Riemannian maps to Kähler manifolds. Int. J. Geom. Methods Mod. Phys. 7 (2010), 337-355. DOI 10.1142/S0219887810004324 | MR 2646767 | Zbl 1193.53148
[26] Tromba, A. J.: Teichmüller Theory in Riemannian Geometry: Based on Lecture Notes by Jochen Denzler. Lectures in Mathematics ETH Zürich Birkhäuser, Basel (1992). MR 1164870 | Zbl 0785.53001
[27] Watson, B.: Almost Hermitian submersions. J. Differ. Geom. 11 (1976), 147-165. DOI 10.4310/jdg/1214433303 | MR 0407784 | Zbl 0355.53037
Search
Partner of
