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D-LINES ON THE SURFACES OF PARALLEL MEAN CURVATURE IN ARBITRARY DIMENSIONAL MANIFOLDS OF CONSTANT CURVATURE

Journal Name:

  • İstanbul Üniversitesi Fen Fakültesi Matematik, Fizik ve Astronomi Dergisi

Publication Year:

  • 1996-1997

Key Words:

Author NameUniversity of AuthorFaculty of Author

AMS Codes:

Abstract (2. Language): 
In this paper, we define D-lines on the surfaces isometricaily immersed in arbitrary dimensional manifolds of constant curvature formally and geometrically after having proved that for ail arc-length parametrized curves C in M1 with the same tangent vector C°eT(M;)p ,Pe M2, the function
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FULL TEXT (PDF): 
PDF icon arastrmx_190866_55-56_pp_189-211.pdf
189-211
  • English

REFERENCES

References: 

[1] B. Y. Chen, On the Surface with Parallel Mean Curvature Vector, Indiana University Mathematics Journal. Vol. 22, No. 7 (1973), P. 655-676.
[2].J. Erbacher, Isometric Immersions of Constant Mean Curvature and Triviality of the Normal Connection, Nagoya Math. J. Vol. 45 (1975), 139-165.
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[3] F. Erkekoglu & H. H. Hacisalihoglu, Surfaces of Parallel Mean Curvature in Four Dimensional Manifolds of Constant Curvature, Commun. Fac. Sci. Univ. Ank. Series A[, V.42, pp.31-38 (1993).
[4] F. Erkekoglu & H. H. Hacisalihoglu, Surfaces of Parallel Mean Curvature in Arbitrary Dimensional Manifolds of Constant Curvature, Stud. Cere. Mat., Tom. 46, Nr. 3, P. 387-391, Bucuresti, 1994.
[5] F. Erkekoglu & H. H. Hacisalihoglu, G-Iines on the Surfaces of Parallel Mean Curvature in Four Dimensional Manifolds of Constant Curvature, Tr. J. of Mathematics, 19 (1995), 223-238. [6] F. Erkekoglu, G-lines on the Surfaces of Parallel Mean Curvature in Arbitrary Dimensional Manifolds of Constant Curvature (Submitted).
[7] F. Erkekoglu, D-lines on the Surfaces of Parallel Mean Curvature in Four Dimensional Manifolds of Constant Curvature (Submitted).
[8] D. A. Hoffman, Surfaces of Constant Mean Curvature in Manifolds of Constant Curvature, J. Differential Geometry, 8 (1973) 161-176.
[9] F. Semin, On Darboux Lines, Rev. Fac. Sci. Univ. Istanbul, A 17 351-383 (1952).

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