1 |
L. J. Alias, A. Ferrandez, and P. Lucas, Surfaces in the 3-dimensional LorentzMinkowski space satisfying ![${\Delta}$ ${\Delta}$](http://ocean.kisti.re.kr/cgi-bin/mimetex.cgi?\small{${\Delta}$}) = A + B, Pacific J. Math. 156 (1992), no. 2, 201-208.
DOI
|
2 |
L. J. Alias, A. Ferrandez, and P. Lucas, Submanifolds in pseudo-Euclidean spaces satisfying the condition = Ax+B, Geom. Dedicata 42 (1992), no. 3, 345-354.
DOI
|
3 |
L. J. Alias, A. Ferrandez, and P. Lucas, Hypersurfaces in space forms satisfying the condition = Ax + B, Trans. Amer. Math. Soc. 347 (1995), no. 5, 1793-1801.
DOI
|
4 |
L. J. Alias and N. Gurbuz, An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures, Geom. Dedicata 121 (2006), 113-127.
|
5 |
L. J. Alias and M. B. Kashani, Hypersurfaces in space forms satisfying the condition , Taiwanese J. Math. 14, no. 5 (2010), no. 5, 1957-1978.
DOI
|
6 |
M. Barros and O. J. Garay, 2-type surfaces in , Geom. Dedicata 24 (1987), no. 3, 329-336.
DOI
|
7 |
E. Cartan, Familles de surfaces isoparametriques dans les espaces a courbure constante, Ann. Mat. Pura Appl. 17 (1938), no. 1, 177-191.
DOI
|
8 |
E. Cartan, Sur des familles remarquables d'hypersurfaces isoparametriques dans les espaces spheriques, Math. Z. 45 (1939), 335-367.
DOI
|
9 |
E. Cartan, Sur quelque familles remarquables d'hypersurfaces, C. R. Congres Math. Liege (1939), 30-41.
|
10 |
S. Chang, A closed hypersurface of constant scalar curvature and constant mean curvature in is isoparametric, Comm. Anal. Geom. 1 (1993), 71-100.
DOI
|
11 |
S. Chang, On closed hypersurfaces of constant scalar curvatures and mean curvatures in , Pacific J. Math. 165 (1994), no. 1, 67-76.
DOI
|
12 |
B. Y. Chen, Total Mean Curvature and Submanifolds of Finite Type, Series in Pure Mathematics, 1. World Scientific Publishing Co., Singapore, 1984.
|
13 |
B. Y. Chen, Finite Type Submanifolds and Generalizations, University of Rome, Rome, 1985.
|
14 |
B. Y. Chen, Finite type submanifolds in pseudo-Euclidean spaces and applications, Kodai Math. J. 8 (1985), no. 3, 358-375.
DOI
|
15 |
B. Y. Chen, 2-type submanifolds and their applications, Chinese J. Math. 14 (1986), no. 1, 1-14.
|
16 |
B. Y. Chen, Tubular hypersurfaces satisfying a basic equality, Soochow J. Math. 20 (1994), no. 4, 569-586.
|
17 |
B. Y. Chen, A report on submanifolds of finite type, Soochow J. Math. 22 (1996), no. 2, 117-337.
|
18 |
B. Y. Chen, Some open problems and conjectures on submanifolds of finite type: recent development, Tamkang J. Math. 45 (2014), no. 1, 87-108.
DOI
|
19 |
B. Y. Chen, M. Barros, and O. J. Garay, Spherical finite type hypersurfaces, Alg. Groups Geom. 4 (1987), no. 1, 58-72.
|
20 |
B. Y. Chen and M. Petrovic, On spectral decomposition of immersions of finite type, Bull. Austral. Math. Soc. 44 (1991), no. 1, 117-129.
DOI
|
21 |
S. De Almeida and F. Brito, Closed 3-dimensional hypersurfaces with constant mean curvature and constant scalar curvature, Duke Math. J. 61 (1990), no. 1, 195-206.
DOI
|
22 |
F. Dillen, J. Pas, and L. Verstraelen, On surfaces of finite type in Euclidean 3-space, Kodai Math. J. 13 (1990), no. 1, 10-21.
DOI
|
23 |
V. N. Faddeeva, Computational Methods of Linear Algebra, Dover Publ. Inc, 1959, New York.
|
24 |
O. J. Garay, An extension of Takahashi's theorem, Geom. Dedicata 34 (1990), no. 2, 105-112.
DOI
|
25 |
T. Hasanis and T. Vlachos, A local classification of 2-type surfaces in , Proc. Amer. Math. Soc. 112, no. 2 (1991), 533-538.
DOI
|
26 |
T. Hasanis and T. Vlachos, Spherical 2-type hypersurfaces, J. Geometry 40 (1991), no. 1-2, 82-94.
DOI
|
27 |
T. Hasanis and T. Vlachos, Hypersurfaces of satisfying = Ax + B, J. Austral. Math. Soc. Ser. A 53 (1992), no. 3, 377-384.
DOI
|
28 |
S. M. B. Kashani, On some -finite type (hyper)surfaces in , Bull. Korean Math. Soc. 46 (2009), no. 1, 35-43.
DOI
|
29 |
U. J. J. Leverrier, Sur les variations seculaires des elements elliptiques des sept plan'etes principales, J. de Math. s.1 5 (1840), 220-254.
|
30 |
P. Lucas and H. F. Ramirez-Ospina, Hypersurfaces in the Lorentz-Minkowski space satisfying , Geom. Dedicata 153 (2011), 151-175.
DOI
|
31 |
P. Lucas and H. F. Ramirez-Ospina, Hypersurfaces in non-flat Lorentzian space forms satisfying , Taiwanese J. Math. 16 (2012), no. 3, 1173-1203.
DOI
|
32 |
P. Lucas and H. F. Ramirez-Ospina, Hypersurfaces in pseudo-Euclidean spaces satisfying a linear condition on the linearized operator of a higher order mean curvature, Differential Geom. Appl. 31 (2013), no. 2, 175-189.
DOI
|
33 |
P. Lucas and H. F. Ramirez-Ospina, Hypersurfaces in non-flat pseudo-Riemannian space forms satisfying a linear condition in the linearized operator of a higher order mean curvature, Taiwanese J. Math. 17 (2013), no. 1, 15-45.
DOI
|
34 |
M. A. Magid, Lorentzian isoparametric hypersurfaces, Pacific J. Math. 118 (1985), no. 1, 165-197.
DOI
|
35 |
A. Mohammadpouri and S. M. B. Kashani, On some -finite-type Euclidean hypersurfaces, ISRN Geometry 2012 (2012), article ID 591296, 23 pages.
|
36 |
H. Munzner, Isoparametrische hyperflachen in spharen. I and II, Math. Ann. 251 (1980), no. 1, 57-71
DOI
|
37 |
H. Munzner, Isoparametrische hyperflachen in spharen. I and II, Math. Ann. 256 (1981), no. 2, 215-232.
DOI
|
38 |
B. O'Neill, Semi-Riemannian Geometry With Applications to Relativity, Academic Press, New York London, 1983.
|
39 |
J. Park, Hypersurfaces satisfying the equation = Rx+ b, Proc. Amer. Math. Soc. 120 (1994), no. 1, 317-328.
DOI
|
40 |
R. Reilly, Variational properties of functions of the mean curvatures for hypersurfaces in space forms, J. Differential Geom. 8 (1973), 465-477.
DOI
|