Semi-slant Riemannian maps into almost Hermitian manifolds

Kwang-Soon Park; Bayram Şahin

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 4, page 1045-1061
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Park, Kwang-Soon, and Şahin, Bayram. "Semi-slant Riemannian maps into almost Hermitian manifolds." Czechoslovak Mathematical Journal 64.4 (2014): 1045-1061. <http://eudml.org/doc/269835>.

@article{Park2014,
abstract = {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.},
author = {Park, Kwang-Soon, Şahin, Bayram},
journal = {Czechoslovak Mathematical Journal},
keywords = {Riemannian map; semi-slant Riemannian map; harmonic map; totally geodesic map; Riemannian map; semi-slant Riemannian map; harmonic map; totally geodesic map},
language = {eng},
number = {4},
pages = {1045-1061},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Semi-slant Riemannian maps into almost Hermitian manifolds},
url = {http://eudml.org/doc/269835},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Park, Kwang-Soon
AU - Şahin, Bayram
TI - Semi-slant Riemannian maps into almost Hermitian manifolds
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 1045
EP - 1061
AB - 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.
LA - eng
KW - Riemannian map; semi-slant Riemannian map; harmonic map; totally geodesic map; Riemannian map; semi-slant Riemannian map; harmonic map; totally geodesic map
UR - http://eudml.org/doc/269835
ER -

References

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  1. Abraham, R., Marsden, J. E., Ratiu, T., 10.1007/978-1-4612-1029-0, Applied Mathematical Sciences 75 Springer, New York (1988). (1988) MR0960687DOI10.1007/978-1-4612-1029-0
  2. Aprodu, M. A., Aprodu, M., 10.1007/s002290050198, Manuscr. Math. 100 (1999), 103-121. (1999) Zbl0938.53035MR1714452DOI10.1007/s002290050198
  3. Aprodu, M. A., Aprodu, M., Brînzănescu, V., 10.1142/S0129167X0000057X, Int. J. Math. 11 (2000), 1177-1191. (2000) Zbl0978.58006MR1809307DOI10.1142/S0129167X0000057X
  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). (2003) Zbl1055.53049MR2044031
  5. Bejancu, A., Geometry of CR-Submanifolds, Mathematics and Its Applications (East European Series) 23 D. Reidel Publishing Co., Dordrecht (1986). (1986) Zbl0605.53001MR0861408
  6. Burns, D., Burstall, F., Bartolomeis, P. de, Rawnsley, J., 10.4310/jdg/1214443603, J. Differ. Geom. 30 (1989), 579-594. (1989) Zbl0678.53062MR1010173DOI10.4310/jdg/1214443603
  7. Candelas, P., Horowitz, G. T., Strominger, A., Witten, E., Vacuum configurations for superstrings, Nuclear Phys. B (electronic only) 258 (1985), 46-74. (1985) MR0800347
  8. Chen, B.-Y., Geometry of Slant Submanifolds, Katholieke Universiteit Leuven, Dept. of Mathematics, Leuven (1990). (1990) Zbl0716.53006MR1099374
  9. Chen, B.-Y., 10.1017/S0004972700017925, Bull. Aust. Math. Soc. 41 (1990), 135-147. (1990) Zbl0677.53060MR1043974DOI10.1017/S0004972700017925
  10. Chinea, D., 10.1007/BF02844887, Rend. Circ. Mat. Palermo (2) 34 (1985), 89-104. (1985) Zbl0589.53041MR0790818DOI10.1007/BF02844887
  11. Eells, J. J., Sampson, J. H., 10.2307/2373037, Am. J. Math. 86 (1964), 109-160. (1964) Zbl0122.40102MR0164306DOI10.2307/2373037
  12. Esposito, G., 10.1142/S0219887805000752, Int. J. Geom. Methods Mod. Phys. 2 (2005), 675-731. (2005) Zbl1086.83025MR2162076DOI10.1142/S0219887805000752
  13. Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian Submersions and Related Topics, World Scientific, River Edge, New York (2004). (2004) Zbl1067.53016MR2110043
  14. Fischer, A. E., 10.1090/conm/132/1188447, 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. (1992) Zbl0780.53033MR1188447DOI10.1090/conm/132/1188447
  15. García-Río, E., Kupeli, D. N., Semi-Riemannian Maps and Their Applications, Mathematics and Its Applications 475 Kluwer Academic Publishers, Dordrecht (1999). (1999) Zbl0924.53003MR1700746
  16. Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737. (1967) Zbl0147.21201MR0205184
  17. Ianuş, S., Mazzocco, R., Vîlcu, G. E., 10.1007/s10440-008-9241-3, Acta Appl. Math. 104 (2008), 83-89. (2008) Zbl1151.53329MR2434668DOI10.1007/s10440-008-9241-3
  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). (1979) Zbl0407.00015MR0564439
  19. Loubeau, E., Slobodeanu, R., 10.1007/s10711-009-9409-7, Geom. Dedicata 145 (2010), 103-126. (2010) Zbl1194.53055MR2600948DOI10.1007/s10711-009-9409-7
  20. Marrero, J. C., Rocha, J., 10.1007/BF01278477, Geom. Dedicata 52 (1994), 271-289. (1994) Zbl0810.53054MR1299880DOI10.1007/BF01278477
  21. O'Neill, B., 10.1307/mmj/1028999604, Mich. Math. J. 13 (1966), 459-469. (1966) Zbl0145.18602MR0200865DOI10.1307/mmj/1028999604
  22. Papaghiuc, N., Semi-slant submanifolds of a Kaehlerian manifold, An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 40 (1994), 55-61. (1994) Zbl0847.53012MR1328947
  23. Şahin, B., 10.1142/S0219887812500806, Int. J. Geom. Methods Mod. Phys. 10 (2013), Paper No. 1250080, 12 pages. (2013) Zbl1263.53025MR3004125DOI10.1142/S0219887812500806
  24. Şahin, B., 10.1142/S0219887811005725, Int. J. Geom. Methods Mod. Phys. 8 (2011), 1439-1454. (2011) Zbl1242.53039MR2873816DOI10.1142/S0219887811005725
  25. Şahin, B., 10.1142/S0219887810004324, Int. J. Geom. Methods Mod. Phys. 7 (2010), 337-355. (2010) Zbl1193.53148MR2646767DOI10.1142/S0219887810004324
  26. Tromba, A. J., Teichmüller Theory in Riemannian Geometry: Based on Lecture Notes by Jochen Denzler, Lectures in Mathematics ETH Zürich Birkhäuser, Basel (1992). (1992) Zbl0785.53001MR1164870
  27. Watson, B., 10.4310/jdg/1214433303, J. Differ. Geom. 11 (1976), 147-165. (1976) Zbl0355.53037MR0407784DOI10.4310/jdg/1214433303

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