DOI QR코드

DOI QR Code

MINIMAL TRANSLATION SURFACES WITH RESPECT TO SEMI-SYMMETRIC CONNECTIONS IN ℝ3 AND ℝ31

  • Wang, Yong (School of Mathematics and Statistics Northeast Normal University)
  • 투고 : 2020.08.29
  • 심사 : 2021.01.29
  • 발행 : 2021.07.31

초록

In this paper, we define and classify minimal translation surfaces with respect to a kind of semi-symmetric metric connections and a kind of semi-symmetric non-metric connections in ℝ3 and ℝ31.

키워드

과제정보

The author was supported in part by NSFC No.11771070. The author thanks Dr. Sining Wei for her helpful discussions. The author thanks the referee for his (or her) careful reading and helpful comments.

참고문헌

  1. N. S. Agashe and M. R. Chafle, A semi-symmetric nonmetric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 23 (1992), no. 6, 399-409.
  2. N. S. Agashe and M. R. Chafle, On submanifolds of a Riemannian manifold with a semi-symmetric non-metric connection, Tensor (N.S.) 55 (1994), no. 2, 120-130.
  3. A. Cicek Gozutok and E. Esin, Tangent bundle of hypersurface with semi-symmetric metric connection, Int. J. Contemp. Math. Sci. 7 (2012), no. 5-8, 279-289.
  4. S. A. Demirbag, On weakly Ricci symmetric manifolds admitting a semi-symmetric metric connection, Hacet. J. Math. Stat. 41 (2012), no. 4, 507-513.
  5. F Dillen, L. Verstraelen, and G. Zafindratafa, A generalization of the translation surfaces of Scherk, In: Differential geometry in honor of Radu Rosca.K.U.L., pp. 107-109, 1991.
  6. H. A. Hayden, Sub-Spaces of a Space with Torsion, Proc. London Math. Soc. (2) 34 (1932), no. 1, 27-50. https://doi.org/10.1112/plms/s2-34.1.27
  7. T. Imai, Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection, Tensor (N.S.) 23 (1972), 300-306.
  8. T. Imai, Notes on semi-symmetric metric connections, Tensor (N.S.) 24 (1972), 293-296.
  9. J. Inoguchi, R. Lopez, and M.-I. Munteanu, Minimal translation surfaces in the Heisenberg group Nil3, Geom. Dedicata 161 (2012), 221-231. https://doi.org/10.1007/s10711-012-9702-8
  10. H. Liu and Y. Yu, Affine translation surfaces in Euclidean 3-space, Proc. Japan Acad. Ser. A Math. Sci. 89 (2013), no. 9, 111-113. https://doi.org/10.3792/pjaa.89.111
  11. R. Lopez, Minimal translation surfaces in hyperbolic space, Beitr. Algebra Geom. 52 (2011), no. 1, 105-112. https://doi.org/10.1007/s13366-011-0008-z
  12. R. Lopez and M. I. Munteanu, Minimal translation surfaces in Sol3, J. Math. Soc. Japan 64 (2012), no. 3, 985-1003. https://doi.org/10.2969/jmsj/06430985
  13. M. Moruz and M. I. Munteanu, Minimal translation hypersurfaces in ${\mathbb{E}}^4$, J. Math. Anal. Appl. 439 (2016), no. 2, 798-812. https://doi.org/10.1016/j.jmaa.2016.02.077
  14. Z. Nakao, Submanifolds of a Riemannian manifold with semisymmetric metric connections, Proc. Amer. Math. Soc. 54 (1976), 261-266. https://doi.org/10.2307/2040797
  15. K. Seo, Translation hypersurfaces with constant curvature in space forms, Osaka J. Math. 50 (2013), no. 3, 631-641. http://projecteuclid.org/euclid.ojm/1380287426
  16. D. Yang and Y. Fu, On affine translation surfaces in affine space, J. Math. Anal. Appl. 440 (2016), no. 2, 437-450. https://doi.org/10.1016/j.jmaa.2016.03.066
  17. K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586.
  18. D. W. Yoon, Minimal translation surfaces in ℍ2 × ℝ, Taiwanese J. Math. 17 (2013), no. 5, 1545-1556. https://doi.org/10.11650/tjm.17.2013.2425
  19. D. W. Yoon, Weighted minimal translation surfaces in the Galilean space with density, Open Math. 15 (2017), no. 1, 459-466. https://doi.org/10.1515/math-2017-0043
  20. D. W. Yoon, C. W. Lee, and M. K. Karacan, Some translation surfaces in the 3-dimensional Heisenberg group, Bull. Korean Math. Soc. 50 (2013), no. 4, 1329-1343. https://doi.org/10.4134/BKMS.2013.50.4.1329