References
- [1] Paul Baird and John C. Wood, Harmonic Morphisms Between Riemannian Manifolds, Oxford University Press, 2003.10.1093/acprof:oso/9780198503620.001.0001
- [2] Béla Bollobás, Linear Analysis, an introductory course, Second Edition, Cambridge Mathematical Textbooks, Cambridge University Press, 1999.10.1017/CBO9781139168472
- [3] Wladimir-Georges Bosko and Salvatore Capozziello, A Mathematical Journey to Relativity. Deriving Special and General Relativity with Basic Mathematics, Unitext for Physics, Springer-Verlag, 2020.
- [4] Wladimir G. Bosko and Mircea Crâşmăreanu, A Rosen-type bi-metric universe and its physical properties, International Journal of Geometric Methods in Modern Physics, 15 (2018), No. 10, 1850174.
- [5] N. D. Brubaker, J. Camero, O. Rocha Rocha, R. C. Soto, and B. D. Suceavă, A curvature invariant inspired by Leonhard Euler’s inequality R ≥ 2r, Forum Geometricorum, 18 (2018), 119–127.
- [6] N. D. Brubaker, B. D. Suceavă, A Geometric Interpretation of Cauchy-Schwarz inequality in terms of Casorati Curvature, Int. Electron. J. Geom. 11 (2018), 48–51.
- [7] B. Brzycki, M. D. Giesler, K. Gomez, L. H. Odom, B. D Suceavă, A ladder of curvatures for hypersurfaces in the Euclidean ambient space, Houston Journal of Mathematics 40 (4), 1347–1356.
- [8] F. Casorati, Mesure de la courbure des surfaces suivant l’idée commune. Ses rapports avec les mesures de courbure gaussienne et moyenne, Acta Math. 14 (1) (1890), 95–110.10.1007/BF02413317
- [9] Bang-Yen Chen, Pseudo-Riemannian Geometry, δ−Invariants and Applications, World Scientific, 2011.10.1142/8003
- [10] Zdravko Cvetkovski, Inequalities: Theorems, Techniques and Selected Problems, Springer, 2012.10.1007/978-3-642-23792-8_20
- [11] S. Decu, S. Haesen, and L. Verstraelen, Optimal inequalities involving Casorati curvatures, Bull. Transilv. Univ. Braşov, Ser. B Suppl. 14 (2007) 85–93.
- [12] S. Decu, S. Haesen, and L. Verstraelen, Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature, Mathematics, 2020, 8, 251; doi:10.3390/math8020251, www.mdpi.com/journal/mathematics10.3390/math8020251
- [13] M. P. do Carmo, Riemannian Geometry, Birkhäuser, 1992.10.1007/978-1-4757-2201-7
- [14] J. Eells and L. Lemaire, A Report on Harmonic Maps, Bull. London Math. Soc., 10 (1978), 1–68.10.1112/blms/10.1.1
- [15] C.F. Gauss, Disquisitiones circa superficies curvas, Typis Dieterichianis, Goettingen, 1828.
- [16] S. Germain, Mémoire sur la courbure des surfaces, Journal für die reine und andewandte Mathematik, Herausgegeben von A. L. Crelle, Siebenter Band, pp. 1–29, Berlin, 1831.10.1515/crll.1831.7.1
- [17] D. Hilbert, Die Grundlagen der Physik, Konigl. Gesell. d. Wiss. Gottingen, Nachr. Math.-Phys. Kl. 1915, pp. 395–407.
- [18] Bogdan D. Suceavă, A geometric interpretation of curvature inequalities on hypersurfaces via Ravi substitutions in the Euclidean plane, Math. Intelligencer, 40 (2018), no. 2, 50–54.
- [19] B. D. Suceavă, M. B. Vajiac, Estimates of B.-Y. Chens ̑δ-invariant in terms of Casorati curvature and mean curvature for strictly convex Euclidean hypersurfaces, Int. Electron. J. Geom 12(2019), 26–31.
- [20] G. Vîlcu, An optimal inequality for Lagrangian submanifolds in complex space forms involving Casorati curvature. J. Math. Anal. Appl. 465 (2018), 1209–1222.