Kinematic formulas for powers of invariant homogeneous polynomials in real space forms

Kinematic formulas for hypersurfaces in real space forms are investigated. The explicit expressions of kinematic formulas for powers of invariant homogeneous polynomials <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper Q 2"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">Q</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">\mathcal {Q}_{2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> (even degree) on the second fundamental forms are obtained. The formulas obtained are the concrete form of the result of Howard and an extension of the result obtained by Kang, Sakai, Suh in 2005. As corollaries, we derive certain extensions of the Chern-Federder kinematic formula and one of the results given by Chen.