참고문헌
- A. Bejancu, Geometry of CR-Submanifolds, Kluwer Academic Publishers, Dortrecht, 1986.
- R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. https://doi.org/10.1090/S0002-9947-1969-0251664-4
- D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203. Birkhauser, 2002.
- B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifold, Monatsh. Math. 133 (2001), no. 3, 177-195. https://doi.org/10.1007/s006050170019
- B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds II, Monatsh. Math. 134 (2001), no. 2, 103-119. https://doi.org/10.1007/s006050170002
- B. Y. Chen, CR-warped products in complex projective spaces with compact holomorphic factor, Monatsh. Math. 141 (2004), no. 3, 177-186. https://doi.org/10.1007/s00605-002-0009-y
- B. Y. Chen, Geometry of warped product submanifolds: A survey, J. Adv. Math. Stud. 6 (2013), no. 2, 1-43.
- H. Edelsbrunner and J. Harer, Computational Topology: An Introduction, Lecture Notes, Duke University, 2013.
- H. Federer and W. Fleming, Normal and integral currents, Ann. of Math. 72 (1960), 458-520. https://doi.org/10.2307/1970227
- I. Hasegawa and I. Mihai, Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata 102 (2003), 143-150. https://doi.org/10.1023/B:GEOM.0000006582.29685.22
- H. S. Kim and J. S. Pak, Sectional curvature of contact CR-submanifolds of an odd-dimensional unit sphere, Bull. Korean Math. Soc. 42 (2005), no. 4, 777-787. https://doi.org/10.4134/BKMS.2005.42.4.777
- H. S. Kim and J. S. Pak, Certain contact CR-submanifolds of an odd-dimensional unit sphere, Bull. Korean Math. Soc. 44 (2007), no. 1, 109-116. https://doi.org/10.4134/BKMS.2007.44.1.109
- H. S. Kim and J. S. Pak, Certain class of contact CR-submanifolds of an odd-dimensional unit sphere, Taiwanese J. Math. 14 (2010), no. 2, 629-646. https://doi.org/10.11650/twjm/1500405810
- H. S. Kim and J. S. Pak, Scalar curvature of contact CR-submanifolds in an odd-dimensional unit sphere, Bull. Korean Math. Soc. 47 (2010), no. 3, 541-549. https://doi.org/10.4134/BKMS.2010.47.3.541
- H. B. Lawson and J. Simons, On stable currents and their application to global problems in real and complex geometry, Ann. of Math. 98 (1973), 427-450. https://doi.org/10.2307/1970913
- P. F. Leung, On a relation between the topology and the intrinsic and extrinsic geometries of a compact submanifold, Proc. Edinburgh Math. Soc. 28 (1985), no. 3, 305-311. https://doi.org/10.1017/S0013091500017119
- J. Liu and Q. Zhang, Non-existence of stable currents in submanifolds of the Euclidean spaces, J. Geom. 96 (2009), no. 1-2, 125-133. https://doi.org/10.1007/s00022-010-0024-4
- J. S. Pak, J.-H. Kwon, H. S. Kim, and Y.-M. Kim, Contact CR-submanifolds of an odd-dimensional unit sphere, Geom. Dedicata 114 (2005), 1-11. https://doi.org/10.1007/s10711-004-8175-9
- Y. L. Xin, An application of integral currents to the vanishing theorems, Sci. Sinica Ser. A 27 (1984), no. 3, 233-241.
- K. Yano and M. Kon, Structures on Manifolds, World Scientific, 1984.
- X. S. Zhang, Nonexistence of stable currents in submanifolds of a product of two spheres, Bull. Austral. Math. Soc. 44 (1991), no. 2, 325-336. https://doi.org/10.1017/S0004972700029762