CR-Submanifolds of Generalized 𝑓.𝑝.𝑘.-Space Forms

Table 1

Manifold	Ricci tensor of Minimal 𝜉𝛼-horizontal CR-submanifold
𝑀^2𝑛+𝑠(𝐹1,𝐹2,ℱ)	((𝑛−𝑠−1)𝐹1+3𝐹2+∑^𝑠𝑖=1𝐹𝑖𝑖)𝑔(𝜑𝑋,𝜑𝑌)+(𝑛−𝑠)∑^𝑠𝑖,𝑗=1𝐹𝑖𝑗𝜂^𝑖(𝑋)𝜂^𝑗(𝑌)
𝑀^2𝑛+𝑠	14(3𝑐+𝑠+(𝑛−𝑠−1)(𝑐+3𝑠))𝑔(𝜑𝑋,𝜑𝑌)+(𝑛−𝑠)∑^𝑠𝑖,𝑗=1𝜂^𝑖(𝑋)𝜂^𝑗(𝑌)
𝑀(𝑓1,𝑓2,𝑓3)	((𝑛−1)𝑓1+3𝑓2−𝑓3)𝑔(𝑋,𝑌)−𝜂(𝑋)𝜂(𝑌)(3𝑓2+(𝑛−2)𝑓3)
𝑀Sas(𝑐)	141𝑔(𝑋,𝑌)(𝑛(𝑐+3)+𝑐−5)−4(𝑐−1)(𝑛+1)𝜂(𝑋)𝜂(𝑌)
𝑀Ken(𝑐)	141𝑔(𝑋,𝑌)(𝑛(𝑐−3)+𝑐+5)−4(𝑐+1)(𝑛+1)𝜂(𝑋)𝜂(𝑌)
𝑀cosym(𝑐)	14𝑐(𝑛+1)(𝑔(𝑋,𝑌)−𝜂(𝑋)𝜂(𝑌))
𝑀𝐶(𝛼)(𝑐)	14𝑔(𝑋,𝑌)(𝑛(𝑐+3𝛼^2)+𝑐−5𝛼^21)−4(𝑛+1)(𝑐−𝛼^2)𝜂(𝑋)𝜂(𝑌)

Where 𝑀^2𝑛+𝑠(𝐹₁,𝐹₂,ℱ), 𝑀^2𝑛+𝑠, 𝑀(𝑓₁,𝑓₂,𝑓₃), 𝑀_Sas(𝑐), 𝑀_Ken(𝑐), 𝑀_cosym(𝑐), and 𝑀_𝐶(𝛼)(𝑐) denote generalized 𝑓.𝑝.𝑘.-space form, 𝑆-space form, generalized Sasakian space form, Sasakian space form, Kenmotsu space form, cosymplectic space form, and 𝐶(𝛼)-space form, respectively.