Geodesic
Optimal Inequalities, Contact $\delta$-Invariants and Their Applications
Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 2 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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Associated with a $k$-tuple $(n_1,\ldots,n_k)\in \mathcal S(2n+1)$ with $n\geq 1$, we define a contact $\delta$-invariant, $\delta^c(n_1,\ldots,n_k)$, on an almost contact metric $(2n+1)$-manifold $M$. For an arbitrary isometric immersion of $M$ into a Riemannian manifold, we establish an optimal inequality involving $\delta^c(n_1,\ldots,n_k)$ and the squared mean curvature of the immersion. Furthermore, we investigate isometric immersions of contact metric and $K$-contact manifolds into Riemannian space forms which verify the equality case of the inequality for some $k$-tuple.
Classification : 51M16, 53C40, 53C25, 53D15 
@article{BMMS_2013_36_2_a0,
     author = {Bang-Yen Chen and Veronica Martin-Molina},
     title = {Optimal {Inequalities,} {Contact} $\delta${-Invariants} and {Their} {Applications}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2013},
     volume = {36},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2013_36_2_a0/}
}
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%A Veronica Martin-Molina
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%J Bulletin of the Malaysian Mathematical Society
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Bang-Yen Chen; Veronica Martin-Molina. Optimal Inequalities, Contact $\delta$-Invariants and Their Applications. Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2013_36_2_a0/