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<p>The concept of a contact <i>CR</i>-submanifold in a Sasakian manifold (Yano and Kon in Geom Dedicata 10:369-391, 1981) relates deeply to <i>CR</i> geometry, which originated from the study of real hypersurfaces in complex manifolds&#xa0;(Bejancu in Geometry of CR submanifolds. D. Reidel Publishing Company, Dordrecht, 1986). Initially introduced for anti-holomorphic submanifolds in complex space forms (Chen in Int J Math 23(3):1250045, 2012), the <i>CR</i> <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="22_2025_749_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-invariant has recently been extended to Sasakian space forms (Mihai and Presura in J Geom 109:34, 2018). This article establishes an optimal inequality concerning the contact <i>CR</i> <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="22_2025_749_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-invariant on contact <i>CR</i>-submanifolds within the Lorentz-Sasakian space form.</p>

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A precise determination of the contact CR \(\delta \)-invariant for typical submanifolds within a Lorentz-Sasakian space form

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  • 发表日期：

    2025年5月6日

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  • Octavian Postavaru,
  • Ion Mihai

摘要

The concept of a contact CR-submanifold in a Sasakian manifold (Yano and Kon in Geom Dedicata 10:369-391, 1981) relates deeply to CR geometry, which originated from the study of real hypersurfaces in complex manifolds (Bejancu in Geometry of CR submanifolds. D. Reidel Publishing Company, Dordrecht, 1986). Initially introduced for anti-holomorphic submanifolds in complex space forms (Chen in Int J Math 23(3):1250045, 2012), the CR \(\delta \) δ -invariant has recently been extended to Sasakian space forms (Mihai and Presura in J Geom 109:34, 2018). This article establishes an optimal inequality concerning the contact CR \(\delta \) δ -invariant on contact CR-submanifolds within the Lorentz-Sasakian space form.