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The theory of complex submanifolds of complex manifolds began as a separate field in the nineteenth century as the theory of algebraic curves and algebraic surfaces over the complex field. In the early 1930s, E. Kaehler, J. A. Schouten and D. van Dantzig initiated the study of complex manifolds from Riemannian geometric point of view in [15, 19, 20] which led to the creation of Kaehler manifolds. In 1947, A. Weil pointed out in [21] that there exists a tensor field J of type (1,1) on the tangent bundle of a complex manifold M satisfying J 2 = −I . Then in the same year, C. Ehresmann introduced the notion of almost complex manifolds as even-dimensional manifolds which admit such a tensor field J . An almost Hermitian manifold (M, gM , J ) is an almost complex manifold (M, J ) admitting a Riemannian metric gM which is compatible with the almost complex structure J . An (immersed) submanifold of an almost Hermitian manifold (M, gM , J ) is the image of an isometric immersion
φ : (N , gN ) → (M, gM , J )
from a Riemannian manifold (N , gN ) into (M, gM , J ). For a submanifold N of (M, gM , J ), there exist three important classes of submanifolds; namely the classes of complex, totally real and slant submanifolds based on the action of J on the tangent bundle T N of N defined as follows. In terms of the almost complex structure J , a submanifold N of an almost complex manifold (M, J, g) is called a complex submanifold if
J (T p N ) ⊆ T p N