Richard S. Lemence - Institute of Mathematics, College of Science, University of the Philippines, Diliman, Quezon City, Philippines Dennis T. Leyson - Institute of Mathematics, College of Science, University of the Philippines, Diliman, Quezon City, Philippines Marian P. Roque - Institute of Mathematics, College of Science, University of the Philippines, Diliman, Quezon City, Philippines
It is known that the sphere \(S^n\) admits an almost complex structure only when \(n = 2\) or \(n = 6\) . In this paper, we show that the sphere \(S^n\) is a space of constant sectional curvature and using the results of T. Sato in [4], we determine the scalar curvature and the *-scalar curvature of \(S^6\). We shall also prove that \(S^6\) is a non-Kähler nearly Kähler manifold using the Levi-Civita connection on \(S^6\) defined by H. Hashimoto and K. Sekigawa [3]. In [2], A. Gray and L. Hervella defined sixteen classes of almost Hermitian manifolds. We shall define quasi-Hermitian, a class of almost Hermitian manifolds and partially characterize almost Hermitian manifolds that belong to this class. Finally, under certain conditions, we shall show the sphere \(S^6\) is quasi-Hermitian.
Richard S. Lemence, Dennis T. Leyson, Marian P. Roque, On Some Geometric Properties of the Sphere \(S^n\), Journal of Mathematics and Computer Science, 2 (2011), no. 4, 607--618
Lemence Richard S., Leyson Dennis T., Roque Marian P., On Some Geometric Properties of the Sphere \(S^n\). J Math Comput SCI-JM. (2011); 2(4):607--618
Lemence, Richard S., Leyson, Dennis T., Roque, Marian P.. "On Some Geometric Properties of the Sphere \(S^n\)." Journal of Mathematics and Computer Science, 2, no. 4 (2011): 607--618
