Some results on paracontact metric (k, mu)-manifolds with respect to the Schouten-van Kampen connection

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YÜKSEL PERKTAŞ S., De U. C., YILDIZ A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.51, sa.2, ss.466-482, 2022 (SCI-Expanded, Scopus, TRDizin)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 51 Sayı: 2
• Basım Tarihi: 2022
• Doi Numarası: 10.15672/hujms.941744
• Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.466-482
• Anahtar Kelimeler: Schouten-van Kampen connection, paracontact metric (k, mu)-manifolds, Ricci semisymmetric, Einstein manifold, eta-Einstein manifold, solitons, RICCI SOLITONS, STRUCTURE THEOREMS, CONTACT
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• İnönü Üniversitesi Adresli: Hayır

Özet

In the present paper we study certain symmetry conditions and some types of solitons on paracontact metric (k, mu)-manifolds with respect to the Schouten-van Kampen connection. We prove that a Ricci semisymmetric paracontact metric (k, mu)-manifold with respect to the Schouten-van Kampen connection is an g-Einstein manifold. We investigate paracontact metric (k, mu)-manifolds satisfying (sic) . (sic)(cur) = 0 with respect to the Schouten-van Kampen connection. Also, we show that there does not exist an almost Ricci soliton in a (2n + 1)-dimensional paracontact metric (k, mu)-manifold with respect to the Schouten-van Kampen connection such that k > -1 or k < -1. In case of the metric is being an almost gradient Ricci soliton with respect to the Schouten-van Kampen connection, then we state that the manifold is either N(k)-paracontact metric manifold or an Einstein manifold. Finally, we present some results related to almost Yamabe solitons in a paracontact metric (k, mu)-manifold equipped with the Schouten-van Kampen connection and construct an example which verifies some of our results.