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Clairaut anti-invariant submersions from cosymplectic manifolds
Hakan Mete Tastan,Sibel Gerdan Aydin 호남수학회 2019 호남수학학술지 Vol.41 No.4
We investigate the new Clairaut conditions for anti-invariant submersions whose total manifolds are cosymplectic. In particular, we prove the fibers of a proper Clairaut Lagrangian submersion admitting horizontal Reeb vector field are one dimensional and classify such submersions. We also check the existence of the proper Clairaut anti-invariant submersions in the case of the Reeb vector field is vertical. Moreover, illustrative examples for both trivial and proper Clairaut anti-invariant submersions are given.
CLAIRAUT ANTI-INVARIANT SUBMERSIONS FROM COSYMPLECTIC MANIFOLDS
Tastan, Hakan Mete,Aydin, Sibel Gerdan The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.4
We investigate the new Clairaut conditions for anti-invariant submersions whose total manifolds are cosymplectic. In particular, we prove the fibers of a proper Clairaut Lagrangian submersion admitting horizontal Reeb vector field are one dimensional and classify such submersions. We also check the existence of the proper Clairaut anti-invariant submersions in the case of the Reeb vector field is vertical. Moreover, illustrative examples for both trivial and proper Clairaut anti-invariant submersions are given.
On spirallike functions related to bounded radius rotation
Asena Cetinkaya,Hakan Mete Tastan 호남수학회 2022 호남수학학술지 Vol.44 No.1
In the present paper, we prove the growth and distortion theorems for the spirallike functions class $\mathcal{S}_k(\lambda)$ related to boundary radius rotation, and by using the distortion result, we get an estimate for the Gaussian curvature of a minimal surface lifted by a harmonic function whose analytic part belongs to the class $\mathcal{S}_k(\lambda)$. Moreover, we determine and draw the minimal surface corresponding to the harmonic Koebe function.