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Slant and Semi-slant Submanifolds of Some Almost Contact and Paracontact Metric Manifolds

In: Contact Geometry of Slant Submanifolds

Author

Listed:
  • Viqar Azam Khan

    (Aligarh Muslim University, Department of Mathematics)

  • Meraj Ali Khan

    (University of Tabuk, Department of Mathematics)

Abstract

In an almost Hermitian manifold $$(\bar{M}, J, g)$$ ( M ¯ , J , g ) , the almost complex structure J turns a vector field to another vector field perpendicular to it. The impact of this property onto a submanifold M of $$\bar{M}$$ M ¯ yields invariant (complex or holomorphic) and anti invariant (totally real) distributions on M, where a distribution D on M is holomorphic if $$JD_x = D_x$$ J D x = D x for each $$x \in M$$ x ∈ M and totally real if $$JD_x \subset T^\perp _x M$$ J D x ⊂ T x ⊥ M for each $$x \in M$$ x ∈ M . A submanifold M in $$\bar{M}$$ M ¯ is holomorphic (resp. totally real) if the tangent bundle T(M) of M is holomorphic (resp. totally real).

Suggested Citation

  • Viqar Azam Khan & Meraj Ali Khan, 2022. "Slant and Semi-slant Submanifolds of Some Almost Contact and Paracontact Metric Manifolds," Springer Books, in: Bang-Yen Chen & Mohammad Hasan Shahid & Falleh Al-Solamy (ed.), Contact Geometry of Slant Submanifolds, pages 113-143, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-0017-3_5
    DOI: 10.1007/978-981-16-0017-3_5
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