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The purpose of this paper is to study invariant submanifolds of an n-dimensional manifold M endowed with an F-structure satisfying FK+(−)K+1F=0 and FW+(−)W+1F≠0 for 1<W<K, where K is a fixed positive integer greater than 2. The case when K is odd (≥3) has been considered in this paper. We show that an invariant submanifold M˜, embedded in an F-structure manifold M in such a way that the complementary distribution Dm is never tangential to the invariant submanifold ψ(M˜), is an almost complex manifold with the induced F˜-structure. Some theorems regarding the integrability conditions of induced F˜-structure are proved

international journal of mathematics and mathematical sciences

Submanifolds of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$F$"><mml:mi>F</mml:mi></mml:math>-structure manifold satisfying<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$F^{K} + (-)^{K + 1}F = 0$"><mml:mrow><mml:msup><mml:mi>F</mml:mi><mml:mi>K</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mo>−</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>K</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml…

Submanifolds ofF-structure manifold satisfyingFK+(−)K+1