On Generalized Φ- Recurrent of Kenmotsu Type Manifolds

البحث الحالي يدرس تعميم متكرر Φ-  لمنطويات من النوع كينموتسو. هذا البحث عمل على تحديد مركبات المشتقة الاتجاهية لتنسر الانحناء الريماني. بالإضافة الى ذلك، استنتجت الشروط التي تجعل المنطويات من نوع كينموتسو متناظرة محلياً او تمتلك تعميم متكرر  البحث ايضاً استنتج بان المنطويات من النوع كينموتسو المتناظرة محلياً تكون تعميم متكرر Φ-  تحت شرط مناسب والعكس بالعكس. أضف الى ذلك، استنتاج الدراسة للعلاقة بين منطويات اينشتاين ومنطويات متناظرة محلياً من نوع كينموتسو.          The present paper studies the generalized Φ-  recurrent of Kenmotsu type manifolds. This is done to determine the components of the covariant derivative of the Riemannian curvature tensor. Moreover, the conditions which make Kenmotsu type manifolds to be locally symmetric or generalized Φ- recurrent have been established. It is also concluded that the locally symmetric of Kenmotsu type manifolds are generalized recurrent under suitable condition and vice versa. Furthermore, the study establishes the relationship between the Einstein manifolds and locally symmetric of Kenmotsu type manifolds

Vanishing conharmonic tensor of normal locally conformal almost cosymplectic manifold

summary:The main purpose of the present paper is to study the geometric properties of the conharmonic curvature tensor of normal locally conformal almost cosymplectic manifolds (normal LCAC-manifold). In particular, three conhoronic invariants are distinguished with regard to the vanishing conharmonic tensor. Subsequentaly, three classes of normal LCAC-manifolds are established. Moreover, it is proved that the manifolds of these classes are $\eta$-Einstein manifolds of type $(\alpha,\beta)$. Furthermore, we have determined $\alpha$ and $\beta$ for each class

Generalized curvature tensor and the hypersurfaces of the Hermitian manifold for the class of Kenmotsu type

This paper determined the components of the generalized curvature tensor forthe class of Kenmotsu type and established the mentioned class is{\eta}-Einstein manifold when the generalized curvature tensor is flat; theconverse holds true under suitable conditions. It also introduced the notion ofgeneralized {\Phi}-holomorphic sectional (G{\Phi}SH-) curvature tensor and thusfound the necessary and sufficient conditions for the class of Kenmotsu type tobe of constant G{\Phi}SH-curvature. In addition, the notion of{\Phi}-generalized semi-symmetric was introduced and its relationship with theclass of Kenmotsu type and {\eta}-Einstein manifold established. Furthermore,this paper generalized the notion of the manifold of constant curvature anddeduced its relationship with the aforementioned ideas. It finally showed thatthe class of Kenmotsu type exists as a hypersurface of the Hermitian manifoldand derived a relation between the components of the Riemannian curvaturetensors of the almost Hermitian manifold and its hypersurfaces

Outcomes after perioperative SARS-CoV-2 infection in patients with proximal femoral fractures: an international cohort study

Objectives Studies have demonstrated high rates of mortality in people with proximal femoral fracture and SARS-CoV-2, but there is limited published data on the factors that influence mortality for clinicians to make informed treatment decisions. This study aims to report the 30-day mortality associated with perioperative infection of patients undergoing surgery for proximal femoral fractures and to examine the factors that influence mortality in a multivariate analysis. Setting Prospective, international, multicentre, observational cohort study. Participants Patients undergoing any operation for a proximal femoral fracture from 1 February to 30 April 2020 and with perioperative SARS-CoV-2 infection (either 7 days prior or 30-day postoperative). Primary outcome 30-day mortality. Multivariate modelling was performed to identify factors associated with 30-day mortality. Results This study reports included 1063 patients from 174 hospitals in 19 countries. Overall 30-day mortality was 29.4% (313/1063). In an adjusted model, 30-day mortality was associated with male gender (OR 2.29, 95% CI 1.68 to 3.13, p80 years (OR 1.60, 95% CI 1.1 to 2.31, p=0.013), preoperative diagnosis of dementia (OR 1.57, 95% CI 1.15 to 2.16, p=0.005), kidney disease (OR 1.73, 95% CI 1.18 to 2.55, p=0.005) and congestive heart failure (OR 1.62, 95% CI 1.06 to 2.48, p=0.025). Mortality at 30 days was lower in patients with a preoperative diagnosis of SARS-CoV-2 (OR 0.6, 95% CI 0.6 (0.42 to 0.85), p=0.004). There was no difference in mortality in patients with an increase to delay in surgery (p=0.220) or type of anaesthetic given (p=0.787). Conclusions Patients undergoing surgery for a proximal femoral fracture with a perioperative infection of SARS-CoV-2 have a high rate of mortality. This study would support the need for providing these patients with individualised medical and anaesthetic care, including medical optimisation before theatre. Careful preoperative counselling is needed for those with a proximal femoral fracture and SARS-CoV-2, especially those in the highest risk groups. Trial registration number NCT0432364