Sequential behaviors and social ties jointly shape user preferences; however, most prior work models them in isolation and relies on shallow fusion in Euclidean space, which struggles to capture temporal drift and hierarchical social structure. We propose a novel framework; HGT4Rec, a Hyperbolic Graph Transformer for Sequential and Social Recommendation. A graph transformer encodes item-transition dependencies to track evolving preferences along the sequence, while a hyperbolic transformer operates on the social graph to represent long-range and hierarchical influence. We further introduce FusionGRU, an adaptive gating module that integrates the two representations into a unified preference state for Top-K prediction. Experiments on Yelp, iFashion, LastFM show that HGT4Rec delivers substantial improvements over the strongest baseline, achieving +348.22% / +314.86%, +383.21% / +210.19%, and +90.85% / +9.83% in Recall@10 and NDCG@10, respectively. Our results demonstrate the value of combining graph transformers with hyperbolic space modeling and the gated fusion for next-item recommendation in sequential and social settings (our code).