Table 2 Inequalities for different... | Emerald Publishing

Table 2

Inequalities for different submanifolds in a conformal Sasakian space form endowed with a quarter-symmetric connection

SN	$M$	Inequality
(1)	Semi-slant	$ρ_{M} + ρ \leq ‖ H ‖^{2} + \exp (f) \{\frac{c + 3}{4} - \frac{c - 1}{2 m} + \frac{3 (c - 1)}{4 m (m - 1)} (m_{1} + m_{2} \cos^{2} θ_{2})\} + \frac{t r (B)}{m} + \frac{1}{4} ‖ ω^{#} ‖^{2} - \{(Λ_{1} + Λ_{2}) \frac{a}{m} + Λ_{2} (Λ_{1} - Λ_{2}) \frac{b}{m} - (Λ_{2} - Λ_{1}) λ (H)\}$
(2)	Pseudo-slant	$ρ_{M} + ρ \leq ‖ H ‖^{2} + \exp (f) \{\frac{c + 3}{4} - \frac{c - 1}{2 m} + \frac{3 (c - 1)}{4 m (m - 1)} (m_{1} \cos^{2} θ_{1})\} + \frac{t r (B)}{m} + \frac{1}{4} ‖ ω^{#} ‖^{2} - \{(Λ_{1} + Λ_{2}) \frac{a}{m} + Λ_{2} (Λ_{1} - Λ_{2}) \frac{b}{m} - (Λ_{2} - Λ_{1}) λ (H)\}$
(3)	Contact CR	$ρ_{M} + ρ \leq ‖ H ‖^{2} + \exp (f) \{\frac{c + 3}{4} - \frac{c - 1}{2 m} + \frac{3 (c - 1)}{4 m (m - 1)} (m_{1})\} + \frac{t r (B)}{m} + \frac{1}{4} ‖ ω^{#} ‖^{2} - \{(Λ_{1} + Λ_{2}) \frac{a}{m} + Λ_{2} (Λ_{1} - Λ_{2}) \frac{b}{m} - (Λ_{2} - Λ_{1}) λ (H)\}$
(4)	Slant	$ρ_{M} + ρ \leq ‖ H ‖^{2} + \exp (f) \{\frac{c + 3}{4} - \frac{c - 1}{2 m} + \frac{3 (c - 1)}{4 m (m - 1)} (m_{1} + m_{2}) \cos^{2} θ\} + \frac{t r (B)}{m} + \frac{1}{4} ‖ ω^{#} ‖^{2} - \{(Λ_{1} + Λ_{2}) \frac{a}{m} + Λ_{2} (Λ_{1} - Λ_{2}) \frac{b}{m} - (Λ_{2} - Λ_{1}) λ (H)\}$
(5)	Invariant	$ρ_{M} + ρ \leq ‖ H ‖^{2} + \exp (f) \{\frac{c + 3}{4} - \frac{c - 1}{2 m} + \frac{3 (c - 1)}{4 m (m - 1)} (m_{1} + m_{2})\} + \frac{t r (B)}{m} + \frac{1}{4} ‖ ω^{#} ‖^{2} - \{(Λ_{1} + Λ_{2}) \frac{a}{m} + Λ_{2} (Λ_{1} - Λ_{2}) \frac{b}{m} - (Λ_{2} - Λ_{1}) λ (H)\}$
(6)	Anti-nvariant	$ρ_{M} + ρ \leq ‖ H ‖^{2} + \exp (f) \{\frac{c + 3}{4} - \frac{c - 1}{2 m}\} + \frac{t r (B)}{m} + \frac{1}{4} ‖ ω^{#} ‖^{2} - \{(Λ_{1} + Λ_{2}) \frac{a}{m} + Λ_{2} (Λ_{1} - Λ_{2}) \frac{b}{m} - (Λ_{2} - Λ_{1}) λ (H)\}$