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A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds

  • Miroslava Antić EMAIL logo
Published/Copyright: October 20, 2018
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 68 Issue 5

Abstract

We investigate four-dimensional CR submanifolds in six-dimensional strict nearly Kähler manifolds. We construct a moving frame that nicely corresponds to their CR structure and use it to investigate CR submanifolds that admit a special type of doubly twisted product structure. Moreover, we single out a class of CR submanifolds containing this type of doubly twisted submanifolds.

Further, in a particular case of the sphere S6⁢(1), we show that the two families of four-dimensional CR submanifolds, those that admit a three-dimensional geodesic distribution and those ruled by totally geodesic spheres S3 coincide, and give their classification, which as a subfamily contains a family of doubly twisted CR submanifolds.

MSC 2010: 53B25; 53C42; 53C25
Keywords: CR submanifold; nearly Kähler manifold; doubly twisted product; ruled submanifolds

This research was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, project 174012.

  1. Communicated by Július Korbaš

References

[1] ANTIĆ M.: A class of four-dimensional CR submanifolds of the sphere S6⁢(1), J. Geom. Phys. 110 (2016), 78–89.10.1016/j.geomphys.2016.07.014Search in Google Scholar

[2] ANTIĆ M.: Four-dimensional CR submanifolds of the sphere S6⁢(1) with two-dimensional nullity distribution, J. Math. Anal. Appl. 445 (2017), 1–12.10.1016/j.jmaa.2016.07.072Search in Google Scholar

[3] BEJANCU A.: Geometry of CR-Submanifolds, D. Reidel Publ., Dordrecht, 1986.10.1007/978-94-009-4604-0Search in Google Scholar

[4] BOLTON, J.—DILLEN, F.—DIOOS, B.—VRANCKEN, L.: Almost complex surfaces in the nearly Kähler S3×S3, Tôhoku Math. J. 67 (2015), 1–17.10.2748/tmj/1429549576Search in Google Scholar

[5] BOLTON, J.—VRANCKEN, L.—WOODWARD, L. M.: On almost complex curves in the nearly Kähler 6-sphere, Q. J. Math. 45 (1994), 407–427.10.1093/qmath/45.4.407Search in Google Scholar

[6] BUTRUILLE, J. B.: Homogeneous nearly Kähler manifolds. In: Handbook of PseudoRiemannian Geometry and Supersymmetry, RMA Lect. Math. Theor. Phys. 16, Eur. Math. Soc., Zürich, 2010, pp. 399–423.10.4171/079-1/11Search in Google Scholar

[7] DILLEN, F.—VERSTRAELEN, L.—VRANCKEN, L.: Classification of totally real 3-dimensional submanifolds of S6⁢(1) with K≥1/16, J. Math. Soc. Japan 42 (1990), 565–584.10.2969/jmsj/04240565Search in Google Scholar

[8] EJIRI, E.: Totally real submanifolds in a 6-sphere, Proc. Am. Math. Soc. 83 (1981), 759–763.10.1090/S0002-9939-1981-0630028-6Search in Google Scholar

[9] GRAY, A.: The structure of nearly Kähler manifolds, Math. Ann. 223 (1976), 233–248.10.1007/BF01360955Search in Google Scholar

[10] GRAY, A.—HERVELLA, L. M.: The sixteen classes of almost Hermitian manifold and their linear invariants, Ann. Math. Pura App. 123 (1980), 35–58.10.1007/BF01796539Search in Google Scholar

[11] HARVEY, R.—LAWSON, H. B.: Calibrated Geometries, Acta Math. 148 (1982), 47–157.10.1007/BF02392726Search in Google Scholar

[12] NAGY, P. A.: Nearly Kähler geometry and Riemannian foliations, Asian J. Math. 6 (2002), 481–504.10.4310/AJM.2002.v6.n3.a5Search in Google Scholar

[13] PODESTÀ, F.—SPIRO, A.: 6-dimensional nearly Kähler manifolds of cohomogeneity one, J. Geom. Phys. 60, (2010), 156–164.10.1016/j.geomphys.2009.09.008Search in Google Scholar

[14] PONGE, R.—RECKZIEGEL, H.: Twisted products in pseudo-Riemannian geometry, Geom. Dedicata 48 (1993), 15–25.10.1007/BF01265674Search in Google Scholar

[15] SEKIGAWA, K.: Some CR-submanifolds in a 6-dimensional sphere, Tensor, N. S. 41 (1984), 13–20.Search in Google Scholar

[16] UDDIN, S.: On doubly warped and doubly twisted product submanifolds, Int. Electron. J. Geom. 3 (2010), 35–39.Search in Google Scholar

[17] ZHANG, Y.—DIOOS, B.—HU, Z.—VRANCKEN, L.—WANG, X.: Lagrangian submanifolds in the 6-dimensional nearly Kähler manifolds with parallel second fundamental form, J. Geom. Phys. 108 (2016), 21–37.10.1016/j.geomphys.2016.06.004Search in Google Scholar

Received: 2017-05-22
Accepted: 2017-09-22
Published Online: 2018-10-20
Published in Print: 2018-10-25

© 2018 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0175
Keywords for this article
CR submanifold; nearly Kähler manifold; doubly twisted product; ruled submanifolds

Articles in the same Issue

  1. Prof. RNDr. Beloslav Riečan, DrSc., Dr.h.c. *NOV. 10, 1936 – †AUG. 13, 2018
  2. On the n × n × n Rubik's Cube
  3. Congruences involving alternating harmonic sums modulo pαqβ
  4. On the proximity of large primes
  5. On the factorizations of cubic polynomials with the same discriminant modulo a prime
  6. Some results on abstract convexity of functions
  7. Remarks on b-Metric and metric-preserving functions
  8. Generalization of Ostrowski inequality for convex functions
  9. On microscopic sets and Fubini Property in all directions
  10. New subfamily of meromorphic multivalent starlike functions in circular domain involving q-differential operator
  11. Application of tan(φ(ξ)/2)-expansion method to burgers and foam drainage equations
  12. Approximate sentinels for diffusion phenomena with pollution
  13. Remarks on a semilinear system in ℝn motivated by difference equations
  14. Oscillation tests for difference equations with several non-monotone deviating arguments
  15. On the regularity of one-sided fractional maximal functions
  16. A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space
  17. A note about Volterra operator
  18. Some reverse and numerical radius inequalities
  19. A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds
  20. Sequential decreasing strong size properties
  21. Approximation of Information Divergences for Statistical Learning with Applications
  22. Wigner's theorem for an infinite set
  23. A note on automorphisms of lie ideals in prime rings
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