[1] EELLS J, SAMPSON J. H. Harmonic mappings of Riemannian manifolds[J]. Amer. J. Math., 1964, 86: 109-160. [2] JIANG G Y. 2-Harmonic maps and their first and second variational formulas[J]. Chinese Ann. Math. Ser. A(7), 1986, 4: 389-402. [3] JIANG G Y. 2-Harmonic isometric immersion between Riemannian manifolds[J]. Chinese Ann. Math. Ser. A(7), 1986, 2: 130-144. [4] BALMU??塁 A, MONTALDO S, ONICIUC C. Properties of biharmonic submanifolds in spheres[J]. J. Geom. Symmetry Phys., 2010, 17: 87-102. [5] BALMU??塁 A, MONTALDO S, ONICIUC C. Classification results and new examples of proper biharmonic submanifolds in spheres[J]. Note Mat., 2008, 28: 49-61. [6] BALMU??塁 A, MONTALDO S, ONICIUC C. Biharmonic hpersurfaces in 4-dimensional space forms[J]. Math. Nachr., 2010, 283: 1696-1705. [7] BALMU??塁 A, MONTALDO S, ONICIUC C. Classification results for biharmonic submanifolds in spheres[J]. Israel J. Math., 2008, 168, 201-220. [8] NAKAUCHI N, URAKAWA H. Biharmonic hpersurfaces in a Riemannian manifold with nonpositive Ricci curvature[J]. Ann. Glob. Anal. Geom., 2011, 40, 125-131. [9] WANG X F, WU L. Proper biharmonic submanifolds in a sphere[J]. Acta Math. Sin. (Engl. Ser)., 2012, 28: 205-218. [10] CADDEO R, MONTALDO S, ONICIUSC S. Biharmonic submanifolds in spheres[J]. Isreal J. Math., 2002, 130: 109-123. [11] ZHANG W. New examples of biharmonic submanifolds in CPn and S2n+1[J]. An. Stiint. Univ. Al. I. Cuza Iasi Mat(N.S.), 2011, 57: 207-218. [12] SASAHARA T. Biharmonic Lagrangian surfaces of constant mean curvature in complex space forms[J]. Glasg. Math. J., 2007, 49: 497-507. [13] VRANCKEN L. Minimal Lagrangian submanifolds with constant sectional curvature in indefinite complex space froms[J]. Proc. Amer. Math. Soc., 2002, 130: 1459-1466. [14] FETCU D, LOUBEAU E, MONTALDO S, et al. Biharmonic submanifolds of CPn[J]. Z. Math., 2010, 266: 505-531. [15] FETCU D. ONICIUC C. Explicit formulas for biharmonic submanifolds in Sasakian space forms[J]. Pacific J. Math., 2009, 24: 85-107. [16] OU Y L, WANG Z P. Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries[J]. J. Geom. Phys., 2006, 228: 185-199. [17] ABRESH U, ROSENBER H. The Hopf differential for constant mean curvature surfaces in S2×R and H2×R[J]. Acta Math., 2004, 193: 141-174. [18] ABRESH U, ROSENBER H. Generalized Hopf differentials[J]. Mat. Contemp., 2005, 28: 1-28. [19] ALENCAR H, DO CARMO M, TRIBUZY R. A Hopf theorem for ambient spaces of dimensions higher than three[J]. J. Differential Geom., 2010, 84: 1-17. [20] FETCU D, ONICIUC C, ROSENBEG H. Biharmonic submanifolds with parallel mean curvature in Sn× R[J]. J. Geom. Anal., 2013, 23: 2158-2176. [21] ROTH J. A note on biharmonic submanifolds of product spaces[J]. J. Geom., 2013, 104: 375C-381. [22] DANIEL B. Isometric immersions into SnR and Hn×R and applications to minimal surfaces[J]. Trans. Amer. Math. Soc., 2004, 361: 6255-6282. [23] DILLEN F, FASTENAKELS J, DER VEKEN VAN J. Surfaces inS2×R with a canonical principal direction[J]. Ann. lobal Anal. Eom., 2009, 35: 381-395. [24] Dillen F., Munteanu M.,: Constant angle surfaces inH2×R[J]. Bull. Braz. Math. Soc. (NS), 2009, 40: 85-97. [25] LI A M, LI J M. An instrinsic rigidity theorem for minimal submanifolds in a sphere[J]. Arch. Math. (Basel), 1992, 58: 582-594.
(上接第299页)
[9] GAN W Z, ZHU P, FANG S W. L2-harmonic 2-forms on minimal hypersurfaces in spheres[J]. Diff. Geom. Appl., 2018,56: 202-210. [10] LI P, WANG J P. Minimal hypersurfaces with fnite index[J]. Math. Res. Lett., 2002, 9: 95-104. [11] HAN Y B. The topological structure of complete noncompact sumanifolds in spheres[J]. J. Math. Anal. Appl., 2018, 457: 991-1006. [12] LI P. Geometric Analysis[M]. Cambridge Stud. Adv. Math., 2012. [13] LI P. On the Sobolev constant and the p-spectrum of a compact Riemannian manifold[J]. Ann. Sci. c. Norm. Supér., 1980, 13: 451-468.
() () |