Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds
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Andreea Olteanu
Abstract
In [An optimal inequality forCR-warped products in complex space forms involvingCRδ-invariant, Internat. J. Math. 23(3) (2012)], B.-Y. Chen introduced the CRδ-invariant for CR-submanifolds. Then, in [Two optimal inequalities for anti-holomorphic submanifolds and their applications, Taiwan. J. Math. 18 (2014), 199–217], F. R. Al-Solamy, B.-Y. Chen and S. Deshmukh proved two optimal inequalities for anti-holomorphic submanifolds in complex space forms involving the CRδ-invariant. In this paper, we obtain optimal inequalities for this invariant for contact CR-submanifolds in almost contact metric manifolds.
(Communicated by Július Korbaš )
References
[1] Alegre, P.—Blair, D. E.—Carriazo, A.: Generalized Sasakian space forms, Israel J. Math. 141 (2004), 157–183.10.1007/BF02772217Search in Google Scholar
[2] Al-Solamy, F.—Chen, B.-Y.—Deshmukh, S.: Two optimal inequalities for anti-holomorphic submanifolds and their applications, Taiwanese J. Math. 18 (2014), 199–217.10.11650/tjm.18.2014.3241Search in Google Scholar
[3] Al-Solamy, F.—Chen, B.-Y.—Deshmukh, S.: Erratum to: Two optimal inequalities for anti-holomorphic submanifolds and their applications, Taiwanese J. Math. 22(3) (2018), 615–616.10.11650/tjm/180405Search in Google Scholar
[4] Atçeken, M.: ContactCR-submanifolds of Kenmotsu manifolds, Serdica Math. J. 37 (2011), 67–78.Search in Google Scholar
[5] Atçeken, M.—Dirik, S.: On contactCR-submanifolds of Kenmotsu manifolds, Acta Univ. Sapientiae Math. 4(2) (2012), 182–198.Search in Google Scholar
[6] Bejancu, A.: Geometry ofCR-Submanifolds, D. Reidel Publishing Company, Dordrecht, Holland, 1986.10.1007/978-94-009-4604-0Search in Google Scholar
[7] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds, Birkhäuser, Boston, 2002.10.1007/978-1-4757-3604-5Search in Google Scholar
[8] Blair, D. E.—Carriazo, A.: The contact Whitney sphere, Note Mat. 20 (2000/2001), 125–133.10.1080/13520806.2000.11758899Search in Google Scholar
[9] Chen, B.-Y.: An optimal inequality forCR-warped products in complex space forms involvingCRδ-invariant, Internat. J. Math. 23(3) (2012), Art. ID 1250045.10.1142/S0129167X12500450Search in Google Scholar
[10] Kenmotsu, K.: A class of almost contact Riemannian manifold, Tohoku Math. J. 24 (1972), 93–103.10.2748/tmj/1178241594Search in Google Scholar
[11] Mihai, I.—Presură, I.: An inequality for contactCR-submanifolds in Sasakian space forms, J. Geom. 109 (2018), Art 34.10.1007/s00022-018-0440-4Search in Google Scholar
[12] Yano, K.—Kon, M.: Structures on Manifolds, World Scientific, Singapore, 1984.10.1142/0067Search in Google Scholar
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Articles in the same Issue
- Regular papers
- Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian?
- Tribonacci numbers with two blocks of repdigits
- Padovan numbers that are concatenations of two distinct repdigits
- On the 2-rank and 4-rank of the class group of some real pure quartic number fields
- A general inverse matrix series relation and associated polynomials – II
- Some hardy type inequalities with finsler norms
- Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives
- Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle
- How is the period of a simple pendulum growing with increasing amplitude?
- Fourier transforms of convolution operators on orlicz spaces
- Some characterizations of property of trans-Sasakian 3-manifolds
- P-Adic metric preserving functions and their analogues
- On statistical convergence of sequences of closed sets in metric spaces
- A characterization of the uniform convergence points set of some convergent sequence of functions
- A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach
- Donsker’s fuzzy invariance principle under the Lindeberg condition
- Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics
- Matrix variate pareto distributions
- Global exponential periodicity and stability of neural network models with generalized piecewise constant delay
- Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds
